When a place is called " Heights", what does "heights" mean/refer to?

It means that area of land is higher then other areas. The Golan heights sits on a plateau above the rest of the surrounding area. Washington heights is named after an old Fort Washington…and the fort was built on top of the highest hill in the area.

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Yep. It's quite literal, also from Wikipedia about Brooklyn heights:

Brooklyn Heights occupies a plateau on a high bluff that rises sharply from the river's edge and gradually recedes on the landward side.

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That's certainly where it comes from. It's not always actually true though. Sometimes someone just liked the name and didn't even think about what it meant.

It's like the name Lakeview. I've been to more than just a couple places named Lakeview something or another. Streets, towns, apartment complexes. The only thing they all had in common is that not a single one of them had a view of a lake.

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- To be fair, I assume you're American and you guys call the main course the entrée. What else can one expect from uncultured barbarians that they don't respect the most basic laws of human decency? I mean, what's next? Wearing a hat inside? Disgusting.
  
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- My town has a “Valley View” that is always amusing. Yeah, it’s at the bottom of a small valley, so there’s no view except the immediately surrounding houses
  
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- We have a bunch of cities here with the word laguna in their name, at least 4 from memory in the same county. No lagunas in sight.
  
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Where I live there is a "College Heights". It is not at a higher elevation, in fact it is one of the lowest areas, nor is it near the college. They just name shit whatever they think will make the most money.

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Usually the community is built on a hill or a mountain. Often times the highest part of the town, geographically. The incline may be gradual or subtle, so you may not notice that it's taller than the rest of the area.

Similarly when streets (in the US) are named High St., it's literally the highest street in town.

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I thought a "high street" was like a commercial strip and didn't refer to literal height

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- I would guess that High Street in the (mostly British?) commercial shopping area sense would have evolved from "highway", meaning a principal or main road, which in turn evolved from "high way", being those roads constructed above grade, so that water would drain off the road into the adjacent ditches. The Romans [citation needed] tended to build all-weather roads like this.
  
  In American English, "highway" would be an odd term to apply to a shopping district -- usually referring to a higher-speed road -- but in some contexts, highway is understood to be any improved road. The California Vehicle Code uses this definition, so that "highway" basically means any public road.
  
  At least in California, roads named High Street do exist, but don't necessarily corespondent to being physically tall over its surroundings or other steets. If anything, a typical High Street is often the same in character as another town's Main Street, which sort-of returns to the British meaning of shopping area again, at least in small towns.
  
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High Street, same as Highway, come from Old English, where high denoted not only elevation, but also status/rank/quality.

You can see this in a lot of other Modern English words. For example, a high sheriff, a high priest or high society aren't called high because they are very tall.

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- ... aren’t called high because they are very tall.
  
  Maybe it's because they smoke a lot of weed.
  
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Over in Calgary Alberta it's mostly rolling hills in the Prairies. Being on a Ridge is a big deal for a housing development.

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High street is an alternative term for Market and used in towns where Market Street is not used. None of them are really the highest street in town, at least not in the US East Coast. The actual elevated places are usually called -view.

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Everyone saying it's taller, but I know for a fact Seaside Heights is not. People who name things name things would ever those people want.

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Hopefully it is higher than the sea.

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- Just enough to give people a false sense of security.
  
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Higher'd'n AC.

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Here's a fun one. I live in a city called Terre Haute. It means "high ground." It's in a river valley.

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Terre Haute has federal death row, Rose-Hulman, and Square Donuts. Am I missing anything?

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- Indiana State University and St. Mary-of-the-Woods University are also here. There's also a fun pet store which is basically a zoo because of all the animals they have that are for looking at, not buying, called Atlantis. There's also a video arcade bar and an all-ages pinball arcade which offers $10 all-play on Friday and Saturday nights.
  
  Overall, I don't like Terre Haute, but it has its pluses.
  
  On the other hand, they're building a casino. Thankfully not on the side of town where I live.
  
  There's also a new concert arena. They recently hosted Ted Nugent. So I won't be paying to go to concerts there.
  
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Things that are high up are associated with status. Naming something "heights" makes people imagine something desirable when they read the name.

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In most towns I’ve been in, it means physical elevation of the district.

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I think most of the time it's just a contrivance to make a place sound fancier. Washington Heights sounds fancier than calling it Washington Drainage Basin. It really doesn't usually have anything to do with the actual elevation of the property.

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See: half the suburbs of Chicago

Chicago Heights, Harwood Heights, Arlington Heights, Highland Park, Palos Heights, etc.

It's purely marketing because they're all flat as fuck

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- Yeah but "Arlington Flat as all Fuck" isn't quite as appealing as "Arlington Heights." It's like adding "Grove" or "Hills" to the end of a town to make it sound more upscale instead of "sits on top of a massive landfill."
  
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there is a town in illinois that was called brickton because chicago brick was dug up there. Now its a hoity toity suburb called park ridge.

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- Brickton definitely lacks much charm as a town name. Most of Utah (where I am) could be called Granitetown for all the granite dug up and used in buildings here. There's a huge quarry where they used to dig up building material, now it's a very fancy and upscale area that costs mega $$ - just to live next to a big pit in the ground.
  
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Washington Heights in NYC, at any rate, is physically high in elevation, and it's not a particularly fancy area at all.

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That's generally how it's used in Australia. There will be an existing suburb named 'generic suburb', and developers will come and build a new housing development full of cookie cutter houses on 300m2 blocks with their gutters near touching eachother and call it 'generic suburb heights' as an attempt to give the schmucks that buy there some sort of feeling of prestige over the older neighbourhood with larger block sizes and more human compatible dwellings.

Other guy in here nailed it with the British origins but for some reason he's been downvoted.

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- Because he put in the same comment, that high street and highway are called that way because they where elevated over the other streets, which is nonsense.
  
  In fact, high street/highway are that way, because in Old English high didn't only denote elevation, but also a high status/rank/importance.
  
  Modern English still uses that meaning, but it's rarer nowadays. For example, high society, high sheriff or high priest aren't called that because they are tall.
  
  High is also used with a lot of words where elevation doesn't matter: high rank, high value and so on.
  
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