Unfinished Tales, as the name implies, is a collection of tales. Also as the name implies, some of these tales are unfinished. They were authored by J.R.R. Tolkien, collated and edited by his son, Christopher Tolkien.
It is required reading for book Tolkien fans, being (probably) the next book most people would read after The Silmarillion, but before embarking on the twelve-volume History of Middle-earth.
UT, as it is usually abbreviated, belongs with the Silm and HoME as being part of Tolkien's 'expanded universe' – unlike Lord of the Rings, there isn't always one definitive version of canon (e.g. the parentage of Gil-Galad, or whether there's one Glorfindel or two, and so on).
Structurally, UT consists of several tales from each of the First, Second, and Third Ages of Middle-earth, some of which are expansions on the published stories in the Silm or LotR (e.g. the Tale of the Children of Hurin), and some of which lie within other parts of the history of Arda (e.g. Aldarion and Erendis, the only completed story from Númenor before its fall). The last section of UT contains some essays on subjects of interest – on the Istari, palantiri, and so on.