Dooku was attempting to shake Obi-Wan's confidence in the Republic and the Jedi, and convince Obi-Wan to join him and the Separatists (allegedly to fight the Sith). The relevant quote is:
Count Dooku: What if I told you that the Republic was now under the
control of a Dark Lord of the Sith?
Obi-Wan: No, that's not possible. The Jedi would be aware of it.
Count Dooku: The dark side of the Force has clouded their vision, my friend. Hundreds of senators are now under the influence of a Sith Lord called Darth Sidious.
Obi-Wan: I don't believe you.
Count Dooku: You must join me, Obi-Wan, and together we will destroy the Sith!
Obi-Wan: I will never join you, Dooku.
Star Wars: Episode II Attack of the Clones, transcribed from a Youtube video of the scene
Dooku didn't actually reveal much information, though. Dooku revealed Palpatine's Sith name, but with no way to connect the Sith name to Palpatine's public persona the name is useless to the Jedi. The information he gave was also misleading: by saying that "hundreds of senators are under the influence" Dooku implied that the Sith Lord was influencing them privately from behind the scenes when in fact the Sith Lord was influencing the Republic Senate in his public capacity as the Supreme Chancellor. Using this information the Jedi might reason that the power of the "hundreds of senators" corrupted by a Sith Lord could be mitigated by giving even more power to the Supreme Chancellor, i.e. the Sith Lord himself.
Since Dooku didn't reveal much information and did so in a misleading way, it was a relatively low risk gamble to attempt to gain Obi-Wan as an ally of the Separatists and possibly trick the Jedi into handing even more power to the Supreme Chancellor.