A very very very close friend of the opposite sex. A woman is a man's platonic friend if she's his best friend (or a very close friend of his), but nothing more.
And yes, contrary to what's been said earlier, men CAN have platonic friends, just like women.
person1: Ashley and Brandon are so close to each other, they spend all of their time together. I'm sure they're dating!
Person2: Not necessarily, i asked Ashley yesterday and she told me that there was nothing between them, they're just platonic friends.