Let’s say you somehow got someone foolish enough to do your every bidding, whatever it may be.
You take him to your studio, grinning, and you force him to do one job, and one job only: you have him hold on to a volume knob for dear life, and every time the sound volume goes above a certain predefined threshold, he should turn the volume down by twisting that knob you chained him to. You instruct him to do so only after a certain time has passed after the threshold was reached – you call this time interval the attack, because you tell that poor man to “attack” the knob to bring down the volume.
You tell him by how much he should turn down the volume when threshold is reached, and you call this the ratio. A “ratio” because it tells him how many times quieter should everything that goes above the threshold be.
You also instruct your man to turn the knob back up a certain time after the volume goes back down below the threshold – you tell him to release the knob, and “release” is what you call this time interval.
To make your poor aid’s work even more difficult, you instruct him to turn the knob at a certain speed, in a “tapered” fashion, and you will call this the knee after you have dismissed your guy for reasons soon revealed, because at this point in the metaphor there’s no possible analogy with a “knee”.
The only reason you put yourself and your aid through so much trouble is so that you can turn the overall volume of your music way up, safe in the knowledge that each peak above the threshold will be swiftly dealt with by your guy riding that volume control. You’ll call this increase makeup gain, because you makeup for what your employee is losing by turning the volume down. In practice, the makeup gain raises the volume only for low-volume parts of your song, because whatever it adds to the other, louder parts, gets promptly trimmed by your volume rider guy.
You then realize that a human riding a volume control will never be quite fast enough to carry out tasks such as those you’ve placed before him. You need something faster, able to work in millisecond land. Oh, yes. Electronics*.
This is all an audio compressor is: an electronic version of a guy riding a volume control really, really fast, according to the basic rules you set for him, thus allowing you to safely increase the overall volume of your music, without fear of nasty clipping.
* You will now be able to visualize the “knee”, too.