A disparaging response, indicating that something previously said was predictable, repetitive or tedious.
This phrase is a modern-day equivalent of 'blah, blah, blah' (which is early 20th century). It is American an emerged during or just after the Second World War. It was preceded by various alternative forms - 'yatata, yatata', 'yaddega, yaddega' etc. The earliest of these that I have found is from an advertisement in an August 1948 edition of the Long Beach Independent:
"Yatata ... yatata ... the talk is all about Chatterbox, Knox's own little Tomboy Cap with the young, young come-on look!"
All of those versions, and including 'yada yada', probably took the lead from existing words meaning incessant talk - yatter, jabber, chatter.
'Yada yada' itself is first found in the 1970s. Dory Previn released the album Mythical Kings and Iguanas in March 1971, which included the song Yada Yada La Scala:
Yada yada La Scala
yada yada yada yada yada
Let’s stop talking talking talking
wasting precious time
Just a lot of empty noise
that isn’t worth a dime
Words of wonder
words of whether
should we shouldn’t we
Yada yada yada yada yada
Lenny Bruce used something very like it in the 1960s in his Essential Lenny Bruce, 1967:
"They're no good, the lot of them - ‘Yaddeyahdah’ - They're animals!"
In the 21st century the place you are most likely to come across it is when installing software; for example, the millions who have installed the Google Toolbar will have seen (although probably not read any further than) the instructions - "Please read this carefully - It's not just the usual yada yada."
See other reduplicated phrases.