1. [n]  computer hardware that sorts data or programs into a predetermined sequence
2. [n]  (biochemistry) an apparatus that can determine the sequence of monomers in a polymer

Any system for recording and/or playback of music via a programmable memory which stores music not as audio data, but as some representation of notes. The most common modern usage of "sequencer" is to refer to systems (whether in software, or as a feature of devices like synthesizers or drum machines) that deal with MIDI data.