Overbreathing a reg simply means you are demanding more gas than you can get from the reg. This is felt as a percieved lag between the time you demand air and the time the reg delivers it. Regretably once this starts the anxiety level of the diver increases, so the air demand increases, which makes the feeling worse, which increases the demand... It's a nasty circle of feedback that often ends in a diver paniced or dead. Note that the reg is STILL providing air, it's just at a slower rate than you want it.
One of the causes is a bad reg design with small passages that restrict air flow at the rate you are demanding it. some low performance regs function fine at shaloow depths, and with relaxed divers. Taking them deep and then working hard fighting a current or fish will often result in overbreathing the reg. This is also the worst possible place and time for the problem
More commonly though this is caused by neglected maintenance or mistuning of an otherwise perfectly good reg. Partially clogged first stage filters are a common error leading to overbreathing.
FT