"Crush Depth" is a term most often used in submarines.

Water is not compressible, so as you go deeper into the ocean, the more the pressure builds up. Lets take snorkeling for example. A snorkel is a little more than a foot long. If you make it much longer than that, you won't be able to breathe. The reason is that if you're like 5 feet down, even with a garden hose in your mouth, there's too much pressure from the water on your body, so you won't be able to expand your chest to inhale. Scuba does it differently.

Submarines have similiar principles. As you go hundreds of feet down, the PSI of water gets fantastically high. Since subs are filled with air, of lesser pressure inside, the pressure outside could crush the vessel like an empty beer can.

A great example of this is in the movie Down Periscope, where they take the old World War II sub to 500 feet. The Dive Officer reminds the captain that it is Crush Depth for this particular ship's class, but they do it anyway. Meanwhile, in the engine room, the engineer ties a string from one end of the hull to the other, and makes it taut (no slack). By the time they get to the depth, the string is hanging very low, meaning the hull just got about a foot narrower. If you're on board, that's a creepy thing.

Modern submersibles don't buckle like that anymore AFAIK. However, the newer submersible vessels, like a Johnson Sea-Link can go into the depths of thousands of feet. The ship used to find the Titanic had to put up with the stress of hundreds of thousands of PSI or more. The glass on these vessels is something like 4 feet thick.