It is a homemade improvised incendiary device consisting of a glass bottle filled with a flammable liquid, such as gasoline, and a cloth wick which acts as a stopper for the bottle as well as the ignition source.
The Molotov cocktail is a single use thrown weapon.
The Molotov cocktail is first available during the mission Molotov Party. In the mission Tommy Angelo is given two to destroy three cars. The Molotov can be encountered later in the mission Great Deal. One of Morello's men standing at the garage entrance has it, and if he is killed before using it, the player can obtain it.
You can find more real world information about the Molotov cocktail on its Wikipedia page.