gain-ratio determines the degree of compression, e.g. 1:1 would be no compression. 2:1 would mean that if the input increased by 2db, the output would only rise 1db.
obviously this results in a lowering of the output, so make-up gain is used to bring the level up to where it was before.
threshold determines when the compression will happen. if the threshold is set high, only the audio peaks will be compressed if it is set to minimum all the signal will be compressed.
there are usually many other controls, but these are the main ones found in all compressors.