Occasionally, you will stumble across, and possibly fall into, a chasm or a large hole in the environment. They are usually 63 blocks deep, but up to 80 blocks deep if surrounded by hills. They sometimes have a 1 or 2 block thick bridge going across them. Usually it is not worthwhile dropping into one as resources are more abundant near the surface and they are a little hard to get out of.
If you are in creative mode, you can simply pillar up, or just use the Jetpack. If you are in explore mode, you can drill a hole in the wall above you, jetpack up to it, drill another hole one block in and drill the blocks directly above you, to provide head room, jetpack up, etc. or, you can mine, and collect, about 60 blocks at ground level and then use those blocks as you would in creative mode.
For moons created after the Update 1.7.0, Chasms have become extremely rare, and perhaps non-existent. Prior to the Update they were fairly common, and moons created prior to the update continue to generate chasms as new areas of your moon are explored.