Grawp is the reason that Hagrid spends most of the year turning up in class with black eyes and bloody noses. He is Hagrid's giant half-brother. At sixteen feet tall, Grawp is shrimpy – for a giant – so the other giants pick on him and beat him up. Now, Hagrid has a long history of picking up dangerous strays – Aragog the giant spider, Norbert the baby dragon – but Grawp is probably the worst. He keeps Grawp hidden in the Forbidden Forest, where the giant hangs around pulling down trees and catching dinner.
Hagrid tries to teach Grawp English, but he's not having much success. He attempts to recruit Harry and Hermione to help him teach Grawp because he is afraid that he is going to booted out of Hogwarts. Needless to say, neither of Harry nor Hermione is eager to start giving a giant language lessons.
But besides the humor of imagining Hermione trying to lecture a giant, Grawp has major plot functions in Order of the Phoenix as well. Grawp is a major cause of contention between Hagrid and the centaurs. Not only are they angry with him for interfering with their punishment of Firenze, but they also don't like sharing the forest with this giant. Hagrid protests that the forest is as much Grawp's as it is the centaurs' (and we're not sure about that – the centaurs were there first), but even relatively kindly Firenze warns Hagrid that "His attempt [to domesticate Grawp] is not working. He would do better to abandon it" (27.61).
As far as plot goes, the presence of Grawp provides a reason for Hagrid to be distracted and occupied during the school year (so he's less of a help to Harry and the rest). Grawp also becomes J.K. Rowling's solution to the centaur showdown at the end of the novel. When Hermione manages to trick Professor Umbridge into following her into the Forbidden Forest, she wants Professor Umbridge to rub the centaurs the wrong way. What she doesn't count on is that the centaurs are so wild and angry that they are willing to attack Hermione and Harry along with Professor Umbridge. Grawp breaks free from the ropes holding him back and comes running up to the herd just in time to distract them from their human captives. So Harry and Hermione have time to run away.
Now, don't get us wrong – Grawp doesn't seem to be blundering up to the centaurs for the sake of Harry and Hermione's health. He wants to find "HAGGER" (33.94) and he recognizes "HERMY" (33.94) as a friend of Hagrid's. When the centaurs see him, they start firing their arrows at him. In a rage, he fights back, and in the ensuing pile-up, Harry and Hermione escape. We will give Hagrid credit for one thing: by the end of the book, Grawp may not be safe or civilized, but he is getting better. He is starting to learn to speak (sort of) and he does seem to have some affection for his half-human brother, Hagrid.