One thing that took awhile to sink in, and made the subject much simpler for me, was getting a mental picture of what "compression" refers to.
Picture dynamics as variation in loudness. Compression means reducing the amount of variation of parts of a signal. "Louder" will often mean "better" in terms of that part of the music, for one thing because its easier for our ears to follow that element, which one hopes is a musical element either rhythmically, melodically, or harmonically.
What makes the subject interesting, and what often takes some thought to get used to, is the idea that this whole subject of compression falls within a realm that is highly non-linear. Non linearity normally refers to measurements where the values one is measuring do not change at a constant rate (in the research I do this can involve rates that increase and then decrease...but most often when something is said to be non-linear it is being measured relative to a single scale, of increase/decrease and when it does not decrease/increase at a constant rate, but at some geometric rate, it is non-linear).
What's important with dynamics involves more than this simple form of non-linearity. It involves the PERCEIVED "space" within the "loudness-quietness realm" that you may want to manage as a musician, producer, mixing board operator, or such. So non-linearity can also be a way of talking about EXPERIENTIAL differences, and not just physically measurable differences (in terms of rates of increase).
An analogy is where a musician who does not do mixing & engineering is thinking in terms of the simple turning of dials on his mixing board. He should be able to coax something nice by simply raising and lowering the levels between the tracks, but for some reason he cannot. This is because the mixing board is designed to represent things in terms of physical and electronic properties. The aesthetic properties are a whole different set of properties, and no one has any way of measuring them, but the talk of compression is an attempt to describe aesthetic IDEALS and basic aesthetic IDEAS of one form or another.
I would liken this to a case where the non-mixing musician has 10 apples, and knows that he wants to reduce them so that there are approximately 5 apples. But since apples are more of a physical idea, rather than the complex aesthetic idea that the mixing engineer is capable of, his idea of apples is a rigid idea. 10 apples equals 10 apples. If he were a chef he might think of them differently.
To a chef, although 5 apples might be half as many apples as 10 apples, if you actually look at your apples, there are different sized ones; in other words the measurement you want to do might be depending on something non-linear, i.e. where one method of equivalency might result in a different answer than another method of equivalency. As I said, the measurements one is attempting to do in terms of improving the aesthetics of various elements of "loudness-quietness realm" are an unknown, and mixing professionals are artists, who are skilled at working within this field based upon their expertise. They realize, when they're truly expert, that loudness is not "better". But that using loudness-quietness is one of the most powerful tools in the palette.
There are a whole series of "firsts" in the manipulation of this loudness-quietness realm dating way back - I've only begun to understand some of them. There are a lot of genre specific techniques. There are also techniques specific to the venue where listening takes place. In listening to classical music in factory-ready car speakers, if the music isn't "compressed" there will be parts where you won't hear what's going on - at all, against the distractions of the outside noises.
Playing guitar, similarly, especially in a single line solo, there are dips in the volume of the notes, after the attack portion of the sound, that will get swallowed up by the distractions of rock music, i.e. drums and bass. Every single genre of music requires a different take on what the aesthetic elements are and how they should best co-exist - which is why its so much fun to begin to use and understand compression.
The AXE FX virtual optical compressors, although making the loudness more consistent and the trail off much slower, has output that contains IMHO much more of the nuance of the actual dynamics. The benefit is that it practically becomes a synthesizer at higher ratios; one can create smooth and flowing timbres.. A 10,000% improvement in that particular genre-specific use, of using a compressor to increase sustain - because for me it prevents the dynamic dullness of too much compression.