Bazinga is a word used by Sheldon Cooper to signal that what he said immediately before this utterance was to be taken as a joke. It’s used by the writers when they can’t figure out a punchline for a joke, so they just let Sheldon say “Bazinga” and cue the laugh track.
The word “Bazinga” was first used in the season 2 season finale, “The Monopolar Expedition” and last in Season 8 episode 15, “The Comic Book Store Regeneration”. (Seasons 6 and 7 are devoid of it.) By this time Sheldon has developed a mediocre sense of humor and instead uses a peculiar form of laughter instead – both literally and sarcastically.