"Meh" is an English interjection (or occasionally, adjective) of extremely recent coinage used to express feelings of apathy, indifference, lack of enthusiasm, lethargy, or mediocrity. It is pronounced with a short "e" as in "bet," with a bit of aspiration at the end, which is why there is an "h".

As an interjection, "meh" primarily indicates apathy or indifference:

"How was the film you saw last night?" -- "Meh. It was okay."

"What would you like to eat for lunch today?" -- "Meh. Anything is fine with me."
In adjectival usage, which is somewhat less common, "meh" indicates lethargy or describes something uninspiring, mediocre, or unexceptional:
"How are you today?" -- "I'm feeling kind of meh."

"How was that concert you went to last night?" -- "It was pretty meh."

Based on how commonly "meh" is used these days in the media, on the internet, and in everyday conversation, I was shocked to realize how new this word is. The earliest verified usage is on a 1995 episode of The Simpsons, "Lisa's Wedding":

MARGE: [weaves on a loom] HI BART, I'M WEAVING ON A LOOM
BART: Meh.
The word "meh" was then used on several subsequent episodes of The Simpsons, most notably in the 2001 episode "Hungry, Hungry Homer":
HOMER: All right, kids, who wants to go to Blockoland?
BART and LISA: Meh.
HOMER: But the commercial gave me the impression that...
BART: We said "meh." LISA: M-E-H: Meh.

According to the OED, the earliest recorded usage of the word "meh" in traditional print media was in the Edmonton Sun, a Canadian newspaper, which ran an article in 2003 containing the following: "Ryan Opray got voted off Survivor. Meh." As far as I can tell from Googling, internet usage does not extend much further back than 2003 either.

Some people have tried to argue that "meh" is a old Yiddish word, but as of yet nobody has been able to show any evidence to prove this, meaning that at least for now, we can probably credit The Simpsons as the origin of this word. But what makes "meh" stand out from so many other neologisms and catchphrases that originated in a Simpsons episode is that unlike those other words, few people seem to realize where "meh" originally came from, and most people seem to be able to intuitively grasp its meaning upon first hearing and quickly integrate it into their everyday vocabulary, even without having seen the Simpsons episodes in question. Thus while some of the other Simpsons buzzwords may fade out of use over time, I'm guessing that "meh" is here to stay.