Some people will claim that a computer is in fact not a DAW at all, and that a DAW is a tool designed specifically for the purpose of making music (ex: a Korg Triton or a Roland Fantom).
Bounce refers to an audio file that you've saved to disk. When you bounce audio, you export one or more tracks to disk for later playback. Bouncing audio is analogous to pre-rendering graphics into a movie.
Bouncing is used often for saving you CPU power. By bouncing, you no longer need to render the track in real-time. In some programs, bouncing an individual track is called freezing the track.
Compression refers to one of two things. Common computer usage refers to "compressing a file" (i.e. making it smaller), of which there are two kinds of compression: lossy and lossless. Lossy compression means throwing away data to make the file smaller. Lossless referes to keeping all of the data intact but making the file smaller (usually with a delay cost).
In audio, compression refers to data, and common compression algorithms are MP3, Ogg Vorbis, AAC, and the (lossless) FLAC.
Compression also refers to audio processing in which you limit the peaks of a signal and expands the lower levels of a signal. You use a compressor for this. Basically, a compressor limits the dynamic range of a signal. Usually, this gives an overall perception of making the sound louder.
Sequencer is a program used for entering (usually) MIDI data. I don't know if it's inherently part of the definition, but most people consider sequencers as allowing you to drag and drop MIDI data to trigger instruments, and as using some kind of piano roll.
A tracker uses a different interface, which usually revolves more around entering note data manually rather than with a visual representation. So entering a note with a tracker usually means that you type in (using a computer keyboard) the length of the note, and what the note is given a text-based representation of the song. My definition could be off but as Gario brought up the main difference between a tracker and a sequencer is the interface.