A double tap is two conductors landed under a single breaker terminal that was designed to hold one. It is one of the most commonly written items on home inspection reports, and it usually appears when someone needed one more circuit and the panel had no spare slots.
The terminal is the reason it matters. A breaker lug is a machined seat sized for a specific conductor range, and a single screw pressing down on it produces even contact across the whole surface. Put two conductors under that screw and the pressure divides unevenly. The thicker or better-positioned one takes most of the clamping force and the other one sits loose.
A loose conductor in a breaker terminal heats under load. That heat is inside a panel, surrounded by other conductors and enclosed in sheet metal, and it can carry on for years before it produces anything visible. When it finally does, the evidence is usually a discoloured lug and a breaker that will not reset.
There is a genuine exception that causes confusion. A small number of breaker models are listed and marked for two conductors, with a terminal designed to seat them side by side. Certain manufacturers make these and the packaging says so explicitly. If a breaker is listed for two, two is correct and no inspector should be writing it up.
The proper fixes are straightforward. Where the panel has room, split the circuits onto separate breakers. Where it does not, a tandem breaker in a slot rated for one gives two circuits in the same space. Where the two conductors genuinely feed the same load, joining them to a single pigtail outside the terminal and landing that pigtail on the breaker gives one conductor under one screw.
None of these is expensive, which is what makes the item worth closing out rather than arguing about. The cost sits entirely in someone opening the panel, and that visit is going to happen anyway when the next circuit gets added.
The neutral bar deserves the same attention while the cover is off. Two neutrals under one terminal is the same problem with the same consequences, and it is often found alongside the breaker version, because whoever added the circuit ran out of room on both bars at the same time.
Worth a read: Home electrical Wiring