Chiburi is translated literally from Japanese as chi (blood) buri (flick). It is the process by which one removes blood from their katana. In Iaido, this is done before placing the blade back into the scabbard (known as noto).

The traditional chiburi position is holding the katana with the right hand, hilt close to the hip, with the tip of the blade pointing downwards and to the left. Most likely in samurai movies and samurai anime you have seen it done as a slash at the empty air, where the blood flies off in a perfect arc. The iaido version is completely ceremonial.

Blood is very hard to get off a katana, even a real chiburi swing usually won't get it off. Most likely if you have blood on your blade, you're going to need to wipe it off. And yes, it is important that you get the blood off before sheathing the blade. The chemicals in blood will not only damage the polish but may eventually start eating away at the metal, which will damage the edge of your weapon.

Not that I know from personal experience or anything like that. Err. Heh.