The name Malfoy is derived from the French mal foie or mal foy, meaning bad faith or unfaithful. He is of course faithful only to Lord Voldemort.
When Lord Voldemort first came to power, Malfoy joined him. When Voldemort fell, the Malfoys claimed they'd been bewitched.
Though this explanation was accepted by the Ministry of Magic, some, such as Arthur Weasley, believed it was a lie, which it was.
Through giving money to charitable causes, Lucius has become very well connected and frequently uses his influence to further his own ends. At one time, Lucius Malfoy was a school governor.
Before his son's, and Harry's, second year, he brewed an elaborate plan which consisted of planting the old school diary of Tom Riddle, also known as Lord Voldemort, on Ginny Weasley, knowing full well that it would possess her and attempt to use her body to open the Chamber of Secrets and attack mudbloods and half-bloods. It his hinted that his target was not the mudbloods, half-bloods or even Ginny, but to discredit Arthur Weasley and thus sabotage the Muggle protection act Weasley had recently proposed.
Malfoy's plan went way beyond success: even what initially was the sole flaw- Malfoy's House-Elf, Dobby, who snuck out of the house to warn Harry of the impending terrible events- failed to tip him off about the true source behind what was about to transpire. Students, animals and ghosts were systematically petrified by Voldemort using Ginny, whose possession became gradually stronger. With moderate pressure from Malfoy (in the form of their families being attacked if they were not to do this), the school governors voted to dismiss Dumbledore as inadequate for running the school.
The plan failed, however, when Riddle decided to pursue his own goals, and rather than continue to petrify the non-purebloods of the school he set his eyes on the destruction of Harry Potter, the boy that Ginny told him would kill him in his future, as a temporally twisted sort of revenge. Ginny finally stopping to trust her diary and throwing it to consequently be found by Harry worked excellently for Riddle, but not at all for Malfoy; this culminated at Riddle putting Malfoy's whole plan at stake in forcing Ginny into the chamber in hopes of Harry trying to rescue her only to be attacked by Riddle and destroyed. As Harry actually was the one to survive the showdown in the chamber (with indirect help from Dumbledore), he was able to discover the truth behind Ginny "attacking" the school students, both proving her innocence and pointing an accusing finger at the true culprit- Malfoy, who was consequently sacked as a school governor. Adding insult to injury, Harry also managed to trick Malfoy into setting Dobby free.
When Lord Voldemort rose again, Malfoy joined him, claiming that he had done everything he could all along to find Voldemort and help him rise again. Voldemort believed him (at least partially), and since Voldemort has a special ability to know when he is being lied to, it is probably true. Even though Harry witnessed Malfoy's declaration of loyalty to Voldemort, pretty much nobody in the ministry believed him and Malfoy continued maintaining strong ties to very high places in the ministry (most prominently in the form of financial support, as has been in the past).
Malfoy was also involved in the battle in the Department of Mysteries, as the apparent leader of the squad sent to pry a crucial prophecy from Harry's hands. He was seen by a myriad of Ministry officials called by Dumbledore to the scene, and- now with irrefutable evidence pointing to his identity as a death eater- promptly sent to Azkaban prison. The Dementors, however, are leaning towards Voldemort's side, and soon Malfoy may be free again.
In the movie, Malfoy is played by Jason Isaacs.