Depending who you ask, choking was used for any\all of the following.
Cool the engine with a gulp of fuel.
Shut the engine down at high RPM on a lap where it’s not needed (ie conserve).
Add fuel to compensate for running lean on exit of tight turns.
Add fuel (oil) to the engine before closing the throttle at 19-20,000 RPM
As to the efficacy of each, again that depends who you ask.
Basically they were capable of revving themselves to mechanical destruction if you let them. Peak performance also tended to coincide with running them right at the edge of mechanical destruction, especially with aircooled. If not that, then just plain locking the motor up from running to lean. Choking was a good way to conserve when you could. Running unleaded fuel didn’t help either.
When watercooled came in (I think '01? @NikG? ), reeds also were introduced to FA and FSA, reeds don’t take kindly heavy choking by comparison to the rotaries in the videos.
Nowadays we have engines that are mostly low(er) revving reeds with piston life in hours rather than minutes so you don’t see it as much.