Threshold - the level at which the compressor switches "on" and acts upon the signal
Attack - determines how quickly the compressor acts upon the signal once it surpasses the threshold - faster attack settings generally sound "smoother" with less transients and punch, and slower attacks generally sound punchier and more aggressive.
Release - determines how quickly the compressor lets go of the signal once it falls below the threshold
Ratio - determines the amount of input signal required for a 1dB increase in output
Think of a compressor as an automatic volume knob. When signal surpasses the threshold level, the compressor turns it down. If the signal doesn't surpass the threshold level, the compressor doesn't do anything. The ratio, attack, and release determine the speed and severity of how the compressor acts upon the audio.
A multi-band compressor is simply a set of multiple compressors, each of which works only on a specific range of frequencies (as opposed to one compressor working on the entire signal). This is nice if you want to apply different settings to the lows, mids and highs or just isolate a problem set of frequencies.
A limiter is simply a compressor with a high "ratio" setting, meaning that it will apply more compression/gain reduction than a lower ratio setting would with the same input level (meaning that if you send the same signal through a compressor with a 4:1 ratio and a limiter with a 20:1 ratio, the limiter will turn the volume down more than the compressor).
A clipper actually reshapes the waveform to eliminate its peaks in order to create headroom to make the signal louder.
