Z-Levels are the various maps with set borders that contain the playable areas of SS13. Moving off the edge of a z-level in space will place you somewhere on the opposite edge of the debris z-level. There are three different z-levels in SS13, each one serving a different purpose.
If you aren't on Oshan Lab, leaving this z-level from any edge will send you to the debris field. If you are, it won't, because the edges are surrounded by unbreakable trench wall. Try going center-ward instead.
A section of deep space long abandoned by Nanotrasen and Syndicate alike, the debris field is loaded with derelict stations, abandoned ships, dangerous attack drones, and plenty of goodies for the adventurous (and well-prepared) scavenger. It's also home to the more habitable Mining Outpost and space diner for those looking for a place to relax off-station.
Leaving the debris field via any edge will place you on the opposite edge of Mining Level (i.e. going off the left edge of debris will put you on the right side of Mining Level). Travelling back to the normal z-level requires a wormhole, teleportation, or the Mining Shuttle (now available on every map).
A mining zone filled with very large, randomly generated asteroids similar to those from the mining magnet. Expect modest bounties of ore, the occasional angry drone, and some very strange, very weird asteroids that'll really leave you scratching your head. You access it by going off the edge of the debris field as described in that section; to go back, it's the same idea. For example, going off the right side of Mining Level will put you on the left side of the debris field, going off the north side will send you to the south side, and vice versa.
A supremely dark, elaborate, randomly-generated underwater cave system lurking underneath Oshan Laboratory. Not much of a station presence besides a tiny, pitch black outpost for the Sea Elevator, but there's plenty of reason to be here. Miners explore these caves for ore, Engineers come here to boost the power of their hotspots, and there's something for everyone if you know where to look. If you tread carefully, you might find some truly tremendous treasures, and, if you're lucky, incredible secrets--and their incredibly tremendous guardians.
You enter and exit the Trench simply by riding the Sea Elevator. In an interesting contrast to the Mining Level and Debris Field it "replaces", you can pilot a minisub into the deep hole in the middle of the station z-level or any the smaller holes scattered about the rim of the station. Walking into said holes is also fine and surprisingly not very dangerous.
This z-level contains areas that are only accessible under certain circumstances, such as the Adventure Zones, VR, and Centcom, where the emergency shuttle eventually ends up. Each area is enclosed in its own portion of the z-level, completely separated from its neighbors.
Entering and exiting this z-level by "normal" means is not possible.