I'm glad you asked. It's my favorite class.
Factotum is a base class in Dungeonscape, starting on page 14.
Perks about the Factotum class include:
-ALL skills are class skills. All of them, which means if you wanted to push this, additional skills not contained in the Player Handbook like Iaijitsu Focus, Autohypnosis, Psycraft, Use Psionic Device and Lucid Dreaming can be on their class list.
-The Factotum relies heavily upon only one Stat, Intelligence, for most of the class abilities. This allows for a pretty powerful character compared to other classes that are more dependent upon multiple Stats to be decent.
-The Factotum can cast Arcane spells, eventually learning the spells up to level 7, off of the Sorcerer/Wizard list. The number of spells the Factotum can cast are Weaksauce compared to a straight arcane caster, but the fact that they have access to these spells at all make them very useful and potentially strong.
-The class abilities for the Factotum can do things uniquely that no other class can do:
*At level 1 you may add your INT mod. to any attack, damage or Save.
*At level 1, you may add your Factotum level to any skill you have at least 1 rank in.
*At level 3 you gain your INT mod. to all STR and DEX checks, and skills that work off of STR and DEX.
*At level 5 you gain a Lay on Hands healing ability that also can Turn Undead.
*At level 8 you gain the ability to take an additional Standard Action on your turn.
*At level 11 you gain the ability to Ignore Spell Resistance and Damage Resistance for one round on a single target.
*At level 13, if a single attack would reduce you to 0 or fewer hitpoints, you can choose to ignore it, once per day. You can just look at death and say, "Um... nope".
-There are more useful class abilities such as granting yourself Sneak attack damage, adding your INT mod. to AC, or using 3 of any extraordinary ability from any other base class per day for 10 rounds, but those aren't as significant as the ones I listed above, IMHO.
THE DRAWBACK to Factotum is it requires a very limited mechanic called "Inspiration Points" to pull off most of it's class abilities. Without the use of a feat to get extra, you have 2 IP at level one and 10 IP at level twenty. These IP replenish after every encounter.
So, in summary, Factotum can do a bunch of very awesome things, a very limited number of times per battle and other encounters. A player who uses the Factotum intelligently can do some powerful things.
Factotum in a Gestalt build allows all skills and the ability to do any of the abilities (such as 2 standard actions) to any other class. Imagine a Wizard that could cast 2 powerful spells back to back in a single round or other similar creative things and you can see the use of a Factotum on the other side of a Gestalt.