"LMAO" is an acronym for "Laughing My Ass Off" or "Laughed My Ass Off." The phrase most likely originated on the Internet.
Shortened forms of words and acronyms have been an integral part of the Internet since the Internet entered popular culture. In fact, "LMAO" has been around at least since 1997, according to the Online Etymology Dictionary. These types of shortcuts allowed online chatters to type faster, thus conveying ideas more quickly. However, they became even more popular with the advent of texting on cellphones, which had limited character space early on. These shortcuts are sometimes called SMS language or textese, as they've established themselves as a part of the English language. Today, textese is still used in online chatting, as well as in texting conversations and Twitter and Facebook updates.