1. (or drop-off) A steep section, or sudden drop on a mountain bike trail.

To be dropped is to be left behind a breakaway or the peloton for whatever reason, usually because the rider cannot sustain the tempo required to stay with the group. To drop someone is to accelerate strongly with the intent of causing following riders to no longer gain the benefit of drafting.

2. (or "Drops") The lower part of the handlebars on a road bike; they run parallel with the top-tube.