Bazinga is used as in interjection on Big Bang Theory where it is used to identify or emphasize a witticism or prank. It has become a catchphrase for the deadpan character of Sheldon, its use something like an announcement that what has just been said has been a joke. The show’s popularity (and perhaps the playfulness of the term) has helped move the word outside of its TV context.
The origins of the term appear to be in the writers’ room of the show:
Sheldon's catchphrase now beloved by fans and nerdy T-shirt companies everywhere got its start as now-showrunner Steven Molaro's catchphrase.
Prady told the audience that during the show's second season, Molaro would use the word to mean "gotcha" when he pulled a trick on a fellow writer.
A "bazinga" was in order, for example, when Molaro gave Prady a grapefruit that turned out to be hollowed out then carefully taped back together. And that's how the catchphrase of smug, trickster Sheldon was born.
— Emily Rome, cnn.com, 14 March 2013
Its use can emphasize the surprise of the moment of recognition:
To an outsider, the RSA algorithm appears like a card trick: You pick a card from a stack, hide it (this is like encryption), and after some manipulations the magician produces your card—bazinga! Well, that’s pretty much what the RSA algorithm does … except that the role of magic is now played by math.
— Edward Frenkel, slate.com, 3 June 2013
Pre-Big Bang Theory use of the word does exist:
You: 'We got snow up to the bazinga last night.'
Topper: 'Hah! Ours was up the wazoo.'
— Saint Paul Pioneer Press, 13 August 2005
Bazinga has also been used to name a newly discovered species of bee, Euglossa bazinga, so named because the bee’s similarity to other species delayed its identification.