The painting is known as "The Dark Tower", by John Howe. Howe is one of the greatest Tolkien illustrators, and worked with Jackson on the movies' art direction.
Originally painted in 1990 for the 1991 Tolkien Calendar, the image depicts Sauron's tower of Barad Dur, in Mordor, with a Lovecraftian spin (it was based on an early Lovecraft-inspired painting Howe had made). It wasn't drawn explicitly for the cover of The Two Towers, so it doesn't necessarily depict a specific scene from that book, but Barad Dur is one of the many choices for the titular Towers in the name of the book.
Having established the Tower being Barad Dur, it came naturally to add a Ringwraith on his flying mount, as they "came more or less with the landscape", according to Howe. Tolkien might not have described these flying mounts precisely - usually just using "The winged Shadow" or "a flying darkness in the shape of a monstrous bird" - but Howe's interpretation (like many of his visual images for Tolkien's works) became the basis for Jackson's vision in the movies.
Here's Howe's commentary, available on his website:
I had (and still do) a collection of photos of the skulls of small animals - mice, rats, small birds - that an art school classmate and I had piled up and photographed. [..] From these snapshots, I had done a painting of the Nameless Isle, from the Dream Quest of Unknown Kadath, by H. P. Lovecraft. [..] Like many things, some paintings are a dry run, and I knew I had the foundations of Sauron's tower Barad-dur.
And here's the full description of the flying creature, from The Return of the King, ch.6 - The Battle of the Pelennor Fields:
[A] winged creature: if bird, then greater than all other birds, and it was naked, and neither quill nor feather did it bear, and its vast pinions were as webs of hide between horned fingers; and it stank. A creature of an older world maybe it was, whose kind, fingering in forgotten mountains cold beneath the Moon, outstayed their day, and in hideous eyrie bred this last untimely brood, apt to evil.