Bonded coins occur when the feeder system, which supplies blank planchets to the coin press, malfunctions and jams. When this occurs, a struck coin is not properly ejected and another planchet is fed into the collar and is struck. This struck coin will land on top of the previously unejected strike and crush and bond together. This may occur many times as more coins bond.

Images courtesy of Byers Numismatic Corp.

Significant examples:
3 Piece Bonded Lincoln Cent on 3 Planchets
(illustrated above).

Sources and/or recommended reading: