Whether we are listening to classical music, jazz, pop, rock, blues, or just about any recorded musical genre we know of, one thing almost always equates to "quality" in a mix - and that is contrast. Our ears need to know what they are hearing, and while our brains are busy deducing information via timbre, pitch, and aesthetic, those of us behind the scenes are responsible for making sure the finished product sounds and feels the way the artists intend.
In the beginning of the recording industry, via wax cylinders came one of the first forms of recorded music, which was more of a "photograph", really - capture the exact live performance as realistically as technology would allow. Of course, today we have, more commonly, a "painting" approach. That is, take the time to create layer upon layer of color, texture, and content which best expresses the intent of the song. One of the most important factors in doing this is contrast.
As an example, we will quite often use a compressor in order to move things forward/backward in a mix. In order to really feel the snare drum, we will compress and bring out the initial transients to get the kick and snare "out ahead" of the rest of the sounds to establish a strong backbeat. This can be done by setting the compressor on the single drum channels or the drum buss to a medium to slow attack and a fast to medium release. This lets the initial crack through, before the compressor grabs the sound and keeps it down. It also helps if the compressor is in itself a bit snappy.
Using compression again, albeit in a different method to create contrast to the snappy drums, we will smooth out the bass to an ever-present low frequency powerhouse and move it back, in order to keep the constant bottom anchor on the frequency spectrum of a track. This can be achieved with a fast to medium attack and a medium to slow release. In this application, it's also good if the compressor is not super aggressive in its way of grabbing the sound, in most cases you'd want a more pillowy and transparent compressor here.
Using panning, we can take midrange-centric multi-tracked electric guitar parts and separate them across the stereo spectrum, so that they create the inviting sense of width that the listener can get lost in, also thereby moving them out of the way of the constant rhythm section which keeps us tapping our feet. The vocals quite often are front and center, demanding our attention right in front of us - the message of the song.
Of course, we have many ways to create tension and further aesthetics in this basic instrumentation example. Very common today in the pop/rock world are all different flavors of saturation/distortion. Whether it be tape emulation (which we equate with a softening of high frequencies and a thickening of the lows), or distortion ranging from subtle harmonic saturation all the way to full-blown overdrive, we have ways to take any element(s) in a mix and tonally separate it from the rest in order to create contrast between different musical parts.
And all of this without getting into one of the most important aspects of all, which is the sense of space which a musical part exists in. Ambience is one of the most obvious musical qualities, and our ears have a remarkable way of distinguishing between musical elements which feel intimate and close - with no reverb at all, or perhaps just a really short room to give some width and dimension - versus those which feel lush and distant. Deciding which parts of a composition will lend themselves to either of these aesthetics (or anywhere in between) is a very important aspect of creative mixing, and thanks to the tools most of us find ourselves with these days, the ability to experiment with them is easier and quicker than ever before.
Even when you listen to a live recording of a band in a room, pay close attention to what it is about the different instruments and musical parts which distinguish themselves naturally from each other, and then consider what you might do creatively to either enhance those distinctions, or minimize them. Although many of us don't pay conscious mind to these sorts of details, it is when we do that we step outside of our comfort zones and begin to approach mixing for what it is - a creative, organic art form.