Editing is the process of taking rendered footage — animation, film, or video — and adjusting how various shots appear in sequence. You typically edit using a nonlinear editor (NLE). An NLE, like Apple's Final Cut Pro or Adobe Premiere, differs from older linear tape-to-tape editing systems that required editors to work sequentially. With an NLE, you can easily edit the beginning of a sequence without worrying too much about it messing up the timing at the end. Blender has basic NLE functions with its Video Sequence Editor.
Compositing is the process of mixing animations, videos, and still images into a single image or video. It's the way that credits show up over footage at the beginning of a movie, or how an animated character is made to appear like she is interacting with a real-world environment. Blender has an integrated compositor that you can use to do these sorts of effects, as well as simply enhance your scene with effects such as blur, glow, and color correction.