Two things you can do to train your ear for compression:
#1. Grab a loop of a drum kit hammering out a medium tempo groove. Compress it using the fastest possible attack and release, ratio around 4 or 5:1, low-ish threshold (getting around -10dB or so of reduction). You'll be hearing a lot of the room sound, but the drums themselves will be contained. Now back off the attack (slow it down) and you'll get transients starting to pop through (and you'll likely have to reduce your make-up gain to avoid clipping the next device in line). Next, slow the release and the room sound will be reduced. The reason you hear so much room with the fast release is that by 'releasing' the gain reduction the unit is effectively 'turning up' the level after the initial reduction,... really fast (so the room sound that is normally below the drum information is effectively gained up before the natural ambience dies away. The slower the attack the more transients are let through (which produces the snapping you hear as you slow the attack).
#2 grab an intimate, uncompressed vocal track. Use 3:1 ratio, fast attack, medium-slow release, adjust threshold to get around -6dB reduction, perhaps a touch more (which is a lot, but we're ear training here, so the greater the reduction the easier it is to hear what is happening). Listen to how close (or not) the vocal 'feels' to the listener. Now relax the attack control, so that more of the leading edges of the consonants get through before the reduction happens. As the attack slows notice what happens to the feeling of intimacy in the vocal track (or put another way, notice how it feels closer as the attack slows and more transients get through unmolested.). Now speed up the release and notice how closer, still, the vocal feels? With slower attack more transients get through, and it feels close. The fast release means the the lower level information at the ends of words and phrases is very present too (again, as the in the drum loop example above, the fast release 'turns up' the level quickly after the initial reduction, which makes it very present).
So a fast attack with medium-slow release will chop the leading transients of words and will keep the low level end-of-phrase information at a lower level = a farther away feeling. Slower attack with fast release will allow more transients through (more in-your-face feeling) and will raise the level of end-of-phrase information, making it too feel more present.
Feel free to use more extreme settings and overall reduction to maximize your ability to hear these things. With the drum loop example it should be pretty easy to 'hear.' With the vocal example it will be more a near/far 'feeling' that you're perceiving. These should get you on your way to training your ear for compression.
Hope this helps.
Joel