A flap tear of the meniscus is a peeling back of part of the one surface of the meniscus.

The flap may be on the upper surface or the undersurface (where it may be missed)
A displaced meniscal tear
These loose flaps may cause intermittent symptoms in the knee. They may also break off and form a 'loose body'.
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CLINICAL PUBLICATIONS
Inferiorly Displaced Flap Tears of the Medial Meniscus MR Appearance and Clinical Significance. Lecas LK, Helms CA, Kosarek FJ and Garret WE. American Journal of Roentgenology, Volume 174, Issue 1.