"Meh" is a verbal shrug. It's vocalized indifference. The very word lacks effort - like whoever created it couldn't be bothered to come up with more than one syllable. It sounds like it came about organically. As if someone just said it one day to describe how they couldn't care less.
However, some believe that the word has Yiddish origins because of it's similarity to the interjection "feh." The word's usage at least goes back as early as 1992 when it was used in an Internet forum discussing the TV show Melrose Place. It was first used in mainstream print by Canadian newspaper, the Edmonton Sun, in 2003. The headline read: "Ryan Opray Got Voted Off Survivor. Meh."
The word really gained popularity after it was used on the uber successful TV show "The Simpsons." It first appeared in the 1992 episode "Homer's Triple Bypass." Homer's daughter, Lisa, uses it to describe how her generation is indifferent to most things, such as her father's open heart surgery.
It was also used in the episodes "Sideshow Bob Roberts," "Lisa's Wedding," and "Hungry, Hungry Homer." The word has been used frequently on another TV show, "The Mentalist," as well. In 2009, BBC named "meh" one of the 20 words that defined the decade.