What are the scenes being portrayed on the covers of the Player's Handbook (PHB), Dungeon Master's Guide (DMG) and Monster Manual (MM) and what monsters do the scenes contain?
The answer can be found on page 2 of all books under the heading On the Cover accompanied by the full image of the cover.
The PHB reads:
In this fiery scene illustrated by Tyler Jacobson, the fire giant King Snurre, suffering no fools to live, calls his hell hounds to join him in confronting unwelcome guests in his home.
The monster on the cover is a Fire Giant (MM p.154) accompanied by Hell Hounds (MM p.182).
King Snurre is…
the final antagonist in the classic Against the Giants modules. Originally used as tournament modules, they were published in 3 parts (G1, G2 and G3) in 1978 and then together (as G1-3) in 1981. The AD&D module G1-3 is available at DMs Guild and a 5E conversion is part of Tales from the Yawning Portal. Versions were also published for other editions of AD&D and D&D.
The DMG reads:
Tyler Jacobson illustrates the arch lich Acererak as he raises an army of undead and prepares to unleash it on an unsuspecting world.
The monster on the cover is a Lich (MM p.202).
the antagonist of the even-more-classic Tomb of Horrors module. Also originally a tournament, it was first published as S1 in 1978. Like G1-3, it is available at DMs Guild and part of Tales from the Yawning Portal.
Acerak has been mentioned in many, many adventures over the last 30 years. Most recently, he is (perhaps) the power behind the Tomb of Annihilation. Maybe. So much contradictory information has been written that it can't all be true. Can it?
The MM reads:
Raymond Swan land illustrates the Xanathar ambushing explorers in the darkest depths of Undermountain, proving that the beholder crime lord's interests run deep beneath the city of Waterdeep.
The monster on the cover is a Beholder (MM p.28).
Xanathar the beholder is…
the leader of the Xanathar Thieves' Guild in Skullport, as described in many sourcebooks and modules. The 5E book Xanathar's Guide to Everything is said to be based on his research and knowledge.