A Giant is a humanoid of extremely large size.
Full-blooded giants are about twenty feet tall (GF24). They are not as intelligent as wizards but are capable of communication, both in their native language and, at times, in English (OP20). They now live mostly in remote mountain areas in tribes, with a leader called a Gurg. They are violent by nature: fights between giants are common, and when a Muggle unsuspectingly wanders into their midst it means certain death. They are also very mistrusting of wizards and magic (OP20).
There was a time when giants were a force to be reckoned with in the wizarding world - there were once at least a hundred different tribes spread out around the globe. In 1926, Newt Scamander saw a giant having a drink in The Blind Pig speakeasy in New York City (WFT).
Then, in the 1970s, the giants allied themselves with Voldemort and were responsible for many of the war's worst incidents of killing and torture, especially of Muggles. Many giants were killed by Aurors and the rest fled into hiding for the next fifteen years.
After Voldemort's return, Albus Dumbledore sent Rubeus Hagrid and Olympe Maxime, both half-giants, to the mountains northeast of Minsk (probably the Urals), as envoys to the eighty or so giants that live there. They found, though, that they were not alone - two Death Eaters, including Walden Macnair, had been sent as envoys for Voldemort, and they ultimately convinced the Gurg, Golgomath, to rejoin Voldemort's forces (OP20). In the summer of 1995, shortly after Voldemort came out of hiding, at least one giant was involved in a Muggle attack in the West Country of England, which was passed off to Muggles as a hurricane (HBP1).
There is one full-blooded giant, however, on the side of the good. While in the mountains, Hagrid discovered he had a half brother living there, and decided to bring him home to Hogwarts. He named him 'Grawp' because "tha's what it sounds like when he says his name" (OP30). Grawp lived in the Forbidden Forest at first and then, after the centaurs got upset, Hagrid moved him to a cave near Hogsmeade. However, Hagrid has been successful in domesticating him somewhat and in teaching him some English - so much so that Grawp was actually able to attend Dumbledore's funeral in spring 1997 ( HBP30).
Unfortunately, partly thanks to the giants' alliance with Voldemort and partly thanks to the wizarding world's general distrust of "part-humans," the giants are looked down upon very heavily. Shortly after Harry witnessed Voldemort's return, Dumbledore tried to convince Cornelius Fudge, then the Minister for Magic, to send envoys to the giants.
Half-giants are looked upon as outcasts by wizards and giants alike; Madame Maxime still refuses to publicly admit her ancestry, and for good reason - when Hagrid's half-giant status leaked out in winter 1994, Rita Skeeter published an article in the Daily Prophet calling for him to be sacked and for Dumbledore's resignation, and Hagrid went into hiding in a feeble attempt to escape the backlash (GF24).
Giants fought on the side of Lord Voldemort at the Battle of Hogwarts, attacking Hogwarts Castle and attempting to crush anyone in their paths (DH31). However they were attacked by Hagrid's half-giant brother Grawp, Buckbeak the Hippogriff as well as the Thestrals from the Forbidden Forest (DH32, DH36). With the defeat of Lord Voldemort, they apparently returned to their remote homelands, but nineteen years after the Battle of Hogwarts, Minister for Magic Hermione Granger had a disturbing report of giants with "winged tattoos" in the Greek Seas (CC1.5), influenced by Voldemort's daughter Delphie who called herself "The Augurey."
The future of the giants is a bleak one - with only eighty or so left in the world, and fights regularly breaking out that severely injure or kill some of those giants that are still around, it is unlikely the race will survive for many more years.