Short answer
A double-tapped breaker is when two electrical conductors are connected under a single breaker lug that is only listed for one conductor. It violates NEC 110.14 in most cases and is one of the most common electrical findings in home inspections.
Long answer
Most breaker manufacturers do not list their breakers for two conductors. Exceptions exist (some Square D QO tandem breakers, certain Cutler-Hammer models) and inspectors confirm the exception by manufacturer specification. When double-tapping is a defect, the recommended correction is installation of a tandem breaker, splitting the circuit into two separate breakers, or pigtailing the conductors at a junction box. Always specify licensed electrician evaluation.