The meanings of both are the same, but the usage is different.
なに (何) can be on its own and means "what."
Example: 何をしていますか? "what are you doing?"
なん (何)is used as a prefix attached to other words to form a phrase. なん is often used in combination with particles, such as the example you gave above: 何時ですか?= "What time is it?"