Deep Cut
This is a colloquial expression referring to a musical track not normally heard on the radio. The track might not have been released as a single, so it’s not in normal rotation, and the deejay (assuming there was one) “cut deep” through the album track list to select it.
Why I Looked It Up
I had heard the phrase before, in musical contexts (I vaguely remember some radio show called “Deep Cut” from my teenage years – it presumably played obscure tracks).
I was painting a porch with my brother (who has always been deeper into music than me). A song I had never heard of came on, and he said “Man, this is a deep cut.” I asked him what it meant.
(I went looking for the name of song – it was something from early Van Halen – but I can’t even find it. It was that deep.)
Postscript
Added on
On a subreddit devoted to dumb things people did when they were kids, the top post is:
In 2004 I won a contest to DJ at my very small hometown’s easy-listening radio station. I proceeded to play an hour of Evanescence deep cuts and ruined everyone’s morning commute.