Abscission is the process by which the leaf gets separated from the tree branch. As stated before, the tree cuts off vital nutrients to the leaves in order to conserve the nutrients for the core, or trunk, of the tree. Abscission is accomplished by specialized cells (denoted as dashed blue lines in image) that build up a barrier between the branch and the leaf's stem. Eventually, these cells wall off the branch from the stem, and as the leaf dies due to lack of nutrition, it falls off.
All you botanists and arborists, feel free to expand upon my oversimplified explanation!