To enumerate is to list or count off one by one. Before you ask for a raise, you'd better be able to enumerate all the reasons why you deserve more money.
Tally, total, add up, compute — however you put it, enumerate is basically just another way to say "count." As in, "How do I love thee? Let me enumerate the ways." This verb came about in the 1610’s as a variation on the Latin enumerates, which means “to reckon up or count over.” To quote Paul Valery, the French critic, essayist, and poet, “Science is feasible when the variables are few and can be enumerated; when their combinations are distinct and clear."