Compressor reduces dynamic range of the sound and is used for balancing shaky vocals, sounds, smoothing clicky drums and raising the average volume of music so that it can be louder without being clipped.

Gain: Amplifies the signal that goes into the volume detector (theshold).

Attack: This is delay (in ms) between the raise of signal above threshold level and start of the compression.

Release: Is time (in ms) the compression will be ended after, once the signal drops below the threshold level.

Threshold: It's a volume level (in db) that is used for triggering the compression.

Ratio: Determines the amount of compression. For example 2:1 means that the amplitude of the sound above the threshold level will be 2 times lower.

Predelay: I don't know what this does.

You can read more about compression from Matt's post on the MPC:

i'm gonna try and be concise here

first off, compression reduces dynamic range. if you imagine a waveform, the distance between peaks and valleys is shrunk.

threshold is the point where compressor kicks in. the ratio of compression is the reduction of dynamic range above the treshold. for example: say threshold = -24 db and ratio = 2:1. everything above -24 db is squished by half, and the output's top signal is now -12 db. stuff below -24 db is not affected.

now you can use gain control to bring the signal back up. using the example above, setting gain to 12 db will restore peaks to 0 db; this will also increase any background noise.

attack determines the length of time before compressor reacts: if it's set to 10 milliseconds, any signal over the threshold shorter than 10 ms will go through unmodified.

release controls the length of time that compressor "holds on" to a level before returning to normal - that is, how long after a peak is detected will compression act for.

hard knee means the compression is linear. soft knee means it's "smooth" or "progressive" (this bit is easy to explain with graphs, if you know what splines are then that's soft knee).

expansion is opposite of compression, it increases dynamic range. controls are pretty much the same. combined with compression, its effect of reducing the strength of signal below the threshold to accentuate the compressed signal even more. high/infinite ratio expansion is essentially a gate, as the stuff below threshold is eliminated.

in case of a kick drum, generally you use a high ratio, start with 4:1 or something like that and work your way up. you need to figure out the threshold yourself, this entirely depends on the sound being compressed. if you're working offline, you can leave gain at zero and normalise afterwards. otherwise, work it out from threshold and ratio.

attack setting depends on what you want to do with the click of the kick: to treat it equally, set it to shortest possible. to leave the click unaffected, work out its length and use that. you can leave release at 250 - 300 ms.

hope this helps