“Infimum” and “Supremum” are mathematical terms that refer to the outer bounds of an ordered set. An infimum is Greatest Lower Bound (GLB), so it is lower than the lowest possible key value. A supremum is the Least Upper Bound (LUB), so it is greater than the greatest possible key value.
InnoDB sets up an infimum record and a supremum record automatically in the root page when an index is first created, and never deletes them. They make a useful barrier to navigation so that “get-prev” won't pass the beginning and “get-next” won't pass the end. Also, the infimum record can be a dummy target for temporary record locks.
The InnoDB code comments distinguish between “the infimum and supremum records” and the “user records” (all other kinds).
The infimum and supremum records can be considered part of the overhead of an index page. Initially, they both exist on the root page, but as the index grows, the infimum record will exist on the first or lowest leaf page and the supremum will the the last record on the last or greatest key page.