In
Star Wars Episode 1,
The Phantom Menace, the bad guy for the showdown was
Darth Maul, the apprentice of the evil
Darth Sidious/Future
Emperor Palpatine. In Episode 2,
Attack of the Clones, the
Bad guy in this is Count Dooku. Played by
Christopher Lee, who also played
Saruman the White in
Lord of the Rings.
The opening titles show that he is the leader of a seperatist group trying to leave the Galactic Senate. His position is so threatening that the senate is seriously considering raising an Army of the Republic to guard against the threat of the Seperatists. Such an action might only invite war. From there the movie begins.
From some of the Dialogue, and if you read The Expanded Star Wars Universe, you can find more about him. He was Yoda's apprentice, and became a very powerful Jedi.
From Starwars.com:
Count Dooku was once a revered Jedi Master whose personal beliefs often clashed with that of the Jedi Council. He believed that the Jedi should not serve so corrupt an institute as the Republic, and 10 years ago, he turned his back on the order, becoming one of the few Jedi to voluntarily renounce his commission. Dooku resurfaced years later as the head of the Separatist movement. His powerful presence and charismatic demeanor have swayed thousands of systems to abandon the Republic in favor of reform.
Qui-Gon Jinn was his apprentice, who apprenticed Obi-Wan Kenobi, who in turn led to Anakin Skywalker/Darth Vader.
From here on it's a Spoiler: He's busy with the trade federation building a robot army to break away, a treasonous act.
Near the end of Attack of the Clones, he retreats, taking the plans for the Death Star to the Emperor. Obi-Wan and Anakin try to stop him, but Dooku uses the power of the Dark side and the Force to hurl bolts of energy at them. There is a lightsaber battle and Anakin gets his arm cut off. Dooku is so corrupted by the Dark Side that he claims "I am the most powerful Jedi ever!" Perhaps Anakin is heading down that path too.
Yoda enters. It's a major showdown, Master versus apprentice. Good versus Evil. Since the same actor from Lord of the Rings does battle again with his powers, many people compare the battles, Saruman vs Gandalf, Dooku vs Yoda. This fight is much better. See the writeup on Yoda for the full description.
Now Dooku is called Darth Tyranus, as he's the apprentice of the Evil emperor Darth Sidious, who helps turn his power towards evil.
Thanks to anotherone, shro0m and Jpers36 for the corrections