The Tube Screamer is an overdrive effect pedal
primarily used with the electric guitar
. As its name suggests, it is made and sold by the Ibanez
Your Screamer does not actually have a tube in it. The name refers to the pedal's original intent, which was to make the tubes in your all-tube amplifier scream. Beautiful, beautiful screaming. Nuts to that solid state amplifier crap... for that, you can use a Boss or DOD stompbox. This is not the pedal to use if you want a heavy metal distortion sound; it's more suited (and intended) for bluesy rock, with that idiom's more organic feel. You metalheads can, again, turn to Boss (especially) for your distortion needs.
Several models have hit the shelves since the inception of the brand name in or around 1978. The first (and, as with most things guitar, subjectively the "best") was the TS-808 (no relation to the 808 drum machine). This was the pedal used by Stevie Ray Vaughan; placing it between a Fender Stratocaster and a Fender Twin Reverb amplifier will get you a good way toward capturing his tone. It is not uncommon to see used 808s priced at around $450.
Next up was the TS-9, first released in 1982. The only significant change in design from the 808 was a revamp of the output stage, which makes the 9 sound relatively "harsher". A capacitor was also added in the switching circuit for noise-suppression reasons. However, this pedal is a lot more common than the 808 and is what most people are referring to when they mention the Tube Screamer. The TS-9 was discontinued circa 1984, but reissued in 1996. Popular opinion goes against the grain here and rates the reissue as highly as the original. Trey Anastasio uses two TS-9s connected in series in his pedal board (into a Twin Reverb amp again); I'm not sure if they're first or second issue, but I would assume the latter. One downside to the TS-9 is that they are not very consistent in tone and quality from pedal to pedal. If you are interested in buying one, try out as many as possible.
There also exists a TS9DX Turbo pedal which, in the words of sideways, is "a regular TS-9 with an extra knob which switches it to emulate some popular mods for regular TS-9 pedals".
Between reissues of the 9, Ibanez was pushing the TS-10 (cheaper), and the TS-5 (yet cheaper and, unfortunately, plastic...this was the first Ibanez pedal I encountered and it turned me off of Ibanez products for some time). The fact that the 9 was reissued is testament to how poorly the 10 and the 5 were received.
One potential drawback to a Tube Screamer is that it is not a "true bypass" pedal. The signal from your guitar travels through the entire circuit of the pedal before being sent to your amp, even when the effect is off. This affects your guitar's tone to some degree, though few people have serious complaints in the case of the Tube Screamer.
http://users.aol.com/AnalogMike/ts9.htm was very helpful.