The Marvel Universe is often used as shorthand to describe one particular universe in a Marvel Multiverse, with infinite different possible worlds also existing alongside it. Some physicists believe that this is how our own universe might actually work, with every choice we make forking into its own unique reality, creating an infinite set of alternate universes.
Even though Marvel comics exists in a multiverse, however, the events that happen in the so-called Marvel Universe usually take place on Earth-616, or in the universe where that planet resides. (Think of Earth-616 as our universe, though it's no more "real" than any other universe.) While there are exceptions, such as X-Men's Age of Apocalypse, most stories in classic Marvel comics happen here.
For semantic reasons, however, "Marvel Universe" should generally be read as shorthand for the Earth-616 universe. (Marvel calls the number that denotes this universe the Official Reality Number.) Even so, Marvel writers and editors apparently don't particularly like to use the term "Earth-616," most often calling the Earth-616 universe the "Marvel Universe" and the Earth-1610 Universe the "Ultimate Universe," so we'll stick with that as well.