It's a contraction of "got to." I gotta get gas = I must get gas or I have to get gas.

"Gotta" is an informal contraction of "got to." It's written this way because in spoken English, when someone says "got to" quickly, it can become "gotta" (just as "see you" is almost always pronounced "see ya"). In terms of etiquette and formality, "have to" is almost always preferable to "got to," "gotta," or "have got to." In other words, if you wish to sound educated, say, "I have to get gas," not "I've gotta get gas" or "I've got to get gas." That said, every rule has exceptions, and with friends, it's fine to say or text, "Gotta go!"