Explicit can mean a variety of things, but we can all agree that for the purposes of this thread, it means unabashedly approaching TABOO [something-or-other], typically race, sex, violence, drugs, religion, politics etc.
Generally, the more popular and commercial the artist, the more such subjects are dealt with through a veil of ambiguities and cryptic lyrics. The flipside to that is obviously music catering to various counterculture movements. Punk rock, hip hop, goth, industrial, metal, lyrical electronic music and all the many subgenres from those roots are ripe with examples, if you look.
That said, during my life, popular music has become more and more explicit and underground music more and more extreme in it's response, not to diminish the impact of older works, mind you.
Racism and Sexism are probably the hottest buttons to push in the eye of the public. Neo Nazi hardcore punk, NSB metal and a *few* industrial / noise have your explicit racism covered though a lot of industrial bands use fascist imagery more for shock than conviction. Sexism is pretty much a cornerstone of both underground and surprisingly publicly popular gansta rap artists, but tends to manifest more viciously in Rape Rock acts like GG Allin and The Mentors. Also worth noting are 'Power Electronics' industrial noise acts like Whitehouse, Genocide Organ, CON DOM and others that seem to have a hangup about women, incorporated into their lyrics.
Religion and Politics can be very explicit in music, but it's not really the same kind of explicit as the above mentioned hot topics. Similarly, drug music is never clinical - it's either celebrating or lamenting substances. The celebration side can be explicit, but it's often more 'take a dose and lose your mind' *taps nose and winks* club music, designed as a soundtrack to chemical induced states at parties. The lamentation side is kinda a different animal - you won't often hear psy trance and grunge rock in the playlist, except on shuffle. Typically you're either hopping around to Infected Mushroom or Hallucinogen, or listening to plaid 90's seattle smack talk, but never at once.
Anyway, I could pull a dozen or so youtube music links down, but since I do that in every other post, it's getting a bit old hat.