The mail was a system for physically transporting postcards, letters, and parcels delivered to a particular address or person.
In 2377, while Tuvok said to Harry Kim that he received a letter from someone named Dennis Kim, his cousin from Earth, who spoke of his mutual friend Maxwell Soroyan, Kim asked if Tuvok read his mail, and Tuvok said "yes". (VOY: "Repression")
Also in 2377, when Tom Paris asked where his mail was, Harry Kim explained everything and Paris said that they couldn't go another month without mail. (VOY: "Inside Man")