It's just one of many words, in many languages, used to denote meaningless or worthless chatter, says Deborah Tannen, a professor of linguistics at Georgetown university. "There so many expressions that all have the same function and often come in threes," she says. "Yada yada yada" is another example.
The Oxford English Dictionary credits the first documented use of "blah" to American journalist Howard Vincent O'Brien, in his 1918 memoir Wine, Women & War - "[He] pulled old blah about 'service'..." Then three years later, the US magazine Collier's: The National Weekly used a double blah - "Then a special announcer begin a long debate with himself which was mostly blah blah."
Usage of "blah blah blah" really spiked in the post-war era, according to Google's NGram program, which measures usage frequency in its collection of digital books. Between 1960 and 2000, it increased 50-fold. That may be in part because it's used repeatedly in print advertising to demonstrate that a company's message stands out from the competition. Or perhaps it's because there's been so much more blabber since then.