Unrelated to Circling Vultures, which foretell a rather worse fate than a mild concussion. Occasionally, more idiosyncratic 'satellites' will circle the character, usually related to either their personality or the task they were trying to accomplish when they were stunned. Similarly, this trope often occurs in live-action instances with just the sound effects of birds. Cartoon cats who see circling birdies sometimes swat at them as though they were real. It is not uncommon for circling stars to sound like birds (cuckoo is very commonly added, although it's usually the cuckoo clock variation instead of the realistic version), even if it makes no sense.
This is a cartoon representation of 'seeing stars.' Upon recovery, the character will usually brush them away with an impatient or brusque sweep of their hands. Sometimes it's just circles or whirls spinning around. An animated character who has been stunned, usually by blunt head trauma, will display a 'halo' of twittering birds or twinkling stars orbiting their head at or above eyebrow level.