Ents are a very old race that appeared in Middle-earth when the Elves did. They were apparently created by Eru Ilúvatar at the behest of Yavanna, after she learned that Aulë's children, the Dwarves, were wont to fell trees. Ents were envisioned as Shepherds of the Trees, to protect the forests from Dwarves and other perils. The Elves have tales of teaching the trees to talk, and that that is how the first Ents came about. Admittedly The Silmarillion is a bit unclear here.
Ents are tree-like creatures, having become like the trees that they shepherd. They vary in traits, from everything to height and size, colouring, and the number of fingers and toes. In the Third Age of Middle-earth, the forest of Fangorn was apparently the only place Ents still lived, although the ent-like Huorns may still have survived elsewhere, as in the Old Forest.
Before that time, almost nothing is known of their history - they apparently lived in and protected the large forests of Middle-Earth in previous ages, and they briefly appear near the end of the First Age, attacking a band of Dwarves, apparently summoned by Beren and Luthien. Treebeard told of a time when apparently all of Eriador was one huge forest and part of his domain, but these immense forests were cut by the Númenóreans of the Second Age.
There used to be Entwives (literally "Ent-women"), but they started to move farther away from the Ents because they liked to plant and control things, so they moved away to the Brown Lands across the Great River Anduin. This area was destroyed by Sauron, and the Entwives disappeared. The Ents looked for them, but have never found them. It is sung by the Ents that one day they will find each other.
They aren't hasty creatures, they take their time, even their language is unhasty. In fact their language appears to be based on an ancient form of Common Eldarin, later enriched by Quenya and Sindarin, although it includes many unique 'tree-ish' additions. It is likely true Entish is unspeakable by any other beings. Ents keep to themselves, except when they are roused to anger.
It is hypothesised that Trollss are corrupted versions of Ents in much the same way that Orcs are corrupted versions of Elves, but the text leaves the facts of the matter ambiguous. Certain is that Treebeard saw Trolls as mockeries of Elves.
In Dungeons & Dragons and the Warcraft PC game, Ents are known as Treants, for copyright reasons. (Just like Hobbits are only referred to as Halflings in D&D.)
The word Ent comes from Middle English, and means giant.
In The Two Towers, Part 2 of Tolkien's novel The Lord of the Rings, the Ents do become angry. They become mad at Saruman because he is getting out of control with power and chopping down their trees. So the Ents have a meeting, or an entmoot. They decide to capture Saruman, or die trying. They are led by Treebeard, the oldest Ent, and Meriadoc Brandybuck and Peregrin Took, two Hobbits who came across Treebeard while trying to escape Saruman's Orcs. They capture Isengard in an all-out assault and trap Saruman in the tower of Orthanc.