Deidara was an S-rank missing-nin from Iwagakure. During his time in the village, he was a member of the Explosion Corps. After defecting from the village, he was the first member, that we know of, that was forced into the Akatsuki. There he was partnered with Sasori until the latter's death, and later with Tobi before his own death.
Deidara was an interesting guy as his main motivation for his destructive ways was his love for his art. He believed that his art was the ultimate form or art so he went to great lengths to prove that to everyone. While usually a cool and collected combatant, he only tended to lose his temper when he felt that someone did not appreciate his art as the best art in the world.
After leaving his village, he was basically a mercenary that worked on his own. His prowess, however, got him noticed by the Akatsuki. Itachi, Sasori, and Kisame all went to recruit him after Orochimaru deserted the group, but were rebuffed by Deidara. Deidara finally accepted to a wager with Itachi. If Deidara were to win his fight against Itachi, then he would be left alone. Unfortunately for Deidara, Itachi defeated him with powerful Genjutsu. This made Deidara obsessed with defeating Itachi, and of course, forced Deidara to join the Akatsuki.
The next time Deidara really appears is in his fight against Gaara. Sasori and he go to retrieve Gaara, with Deidara ending up in a one-on-one fight vs Gaara. During the fight, Deidara has his left arm destroyed by Gaara, but manages to trick Gaara into leaving himself open for an attack. Deidara creates a C-4 bomb that he drops into the middle of the village. Gaara uses his sand powers to protect the village from the attack, but leaves himself open for a sneak attack. Trying to protect himself, Gaara uses his gourd sand to create a protective shell around himself only to find that he has sand has been polluted with Deidara's explosive clay. This is how Deidara captures Gaara.
Deidara then is matched up against Naruto and Kakashi. In this fight Deidara loses his second arm to Kakashi, now leaving him with no arms. Deidara was eventually cornered by Naruto, and narrowly escapes as Naruto's anger boils over and he enters his two-tailed form. He flees and uses a suicide bombing clone in attempt to take out his pursuers.
Later he comes back with both arms reattached by Kakuzu. He now faces off against Sasuke. In his attempt to attack Sasuke, Deidara uses a varying degrees of exploding clay models to test Sasuke's skill. Realizing that Sasuke's level is quite strong, Deidara sees that the only way he can kill Sasuke is in a real suicidal attempt. He exposes the mouth on his chest and turns himself into a suicide bomb. Sasuke, however, gets away with the help of Manda, the giant snake he summoned.
Deidara is an interesting guy because all he really cared was about someone just saying his art was the ultimate art form. This is an interesting idea because in a sense it is very similar to Naruto no?