I'm quite new to all this, but this is my interpretation... am I right in that:
treble = high (frequency) range
mid-range = mid (frequency) range
bass = low (frequency) range
Bass heavy cans would emphasise the low range. This appeals to "bass heads", since they don't mind the extra "punch" at the loss of detail due to muddiness caused by an unnatural low frequency reproduction. (This effect is apparent in most cheaper cans?)
Mid-range cans emphasise the... mid-range. As has been mentioned, this is where "most of the music is". As far as I understand, an emphasised mid-range will make songs sound more natural, but may sacrifice some bass punch & clarity of high notes. (Audio-Technica signature sound?)
Now it's self explanatory what treble emphasising cans would sound like. (Grado signature sound?)
There's also neutral cans, but these seem to be referred to as "boring" nearly everywhere. People seem to want some "coloration", and "mid-range" seems to be the preferred one.
A truly great set of cans (usually $1000+ range) is one that can reproduce each of these ranges with distinction, a "clear" mid-range, "punchy" bass, and "sparkling" treble, without any of the trade off you may see in cheaper cans.
PLEASE CORRECT ME IF ANYTHING SOUNDS ODD! It's just my limited understanding from lurking around here for a few years.
Sorry if this isn't strictly on topic.