"Enterprise" is a fuzzy term that usually means a business-critical system that is deployed across an enterprise, as opposed to a system that supports a single department (though such a system might also be mission-critical). "Enterprise" is also used by Marketing to mean something along the lines of "a system you should expect to pay lots of money for."

It isn't at all surprising that IBM and Microsoft would "reject" MySQL. They're competitors, after all. Expect them to throw up a lot of FUD about MySQL. That said, they do have some valid points: The bigger players have a better transaction and data integrity story, though MySQL is (slowly) catching up.

A truth that IBM and Microsoft would prefer to ignore, though, is that many applications don't need a heavy-duty, full featured RDBMS. A really fast, fairly reliable data access method with SQL support is sufficient for a lot of applications (such as much of what Yahoo does, or discussion boards, or...). For a fairly large set of problems, MySQL is good enough.