To
consummate something means to complete it, to bring it to its final
fruition. In some
Western religious traditions, a marriage is said to be "consummated" when the
couple has
sex for the first time (note that it
is assumed that this is the first time they'll be having sex, and only slightly less so that this is the first time
either one will be having sex). A probable source for this is the
Catholic belief that marriage is fundamentally, though not exclusively, for the purposes of
procreation. If the marriage is not consummated, because either party is
impotent or
unwilling, the marriage can be
annulled on the basis that it's not capable of fulfilling its larger purpose.
Please note: I'm not up on modern Catholic attitudes towards marriage, and I expect that this has changed somewhat in recent decades. The change is probably greatest in the
United States and least or absent in more traditional areas like
Latin America.