I myself would rule that it makes escape attempts on your turn automatically succeed and that even while grappled, you can still attack with weapons normally. This means that you can be grappled (or swallowed whole), but that you aren't suffering as much restriction due to it.
This keeps the spell useful (it is 4th level after all), but also doesn't completely trump all the creatures who have fun, dramatic grapple type attacks. The spell would still protect completely against Evard's black tentacles however, since it is better about cancelling out spells than other things.
I don't think freedom of movement would cancel a paralytic poison, for example.
Due to the wording of the spell though, this is all extremely arguable. I think if someone asked the Sage, his answer would be that freedom of movement does cancel evard's black tentacles, but in no way helps you in a normal grapple situation.
I'm curious about whether it would cancel Otiluke's resilient sphere, if it were very close around the character. I imagine not. Also, I think the Sage's ruling (in the FAQ) on how freedom of movement works underwater makes it nearly worthless for that situation. But now I'm far off topic.