A NLE (non-linear editor) is a common type of a digital video editing program.
Linear editing is the "traditional" way of editing video and movies. You have tapes or film, and you put them together, or cut a section away. Some computer programs (such as VirtualDub) also work same way. The problem in linear editing is that it is very hard to keep track of the correct order of the clips, and making special kinds of transitions from one scene to another is very hard.
Non-linear editing is done on a computer or other digital video production system. You have a number of video clips, and you have a timeline; you can place these clips anywhere on the timeline, add transitions and perharps other effects to it. (Linear editors may also have effect capabilities, though not necessarily as flexible; film can be cut diagonally for sweeps or sweep patterns may be attached on film, tape-based editing can use separate video effect processors, and computer programs like VirtualDub may have have filter/plugin capability.)
The main advantage of non-linear editing is that it's a more pleasant experience because the clips can be rearranged very easily, and the effects don't really apply until the final file is rendered. Changing one clip doesn't affect the others. The effect capabilities are also often more fine-tuned.
Examples of NLE programs:
Source: "Glossary: Video Terms for NLE", by Leitch Technology International; A PDF file somewhere under http://www.dps.com/custserv/dpsdoclib.nsf/667dcdb950a13e718525670c00798075/5b9c2b429ad468b1852569650055b887?OpenDocument - big honkin' URL with session cookie!