In modal logic, ◊ is the possibility operator.
It is possible that P.
For P to be possible is for P to be true in some possible world. Compare ◊P with the modal sentence □P, which means P is true in all possible worlds (necessarily P).1
◊ can be formally defined using □, which is the modal necessity operator, and the negation operator ¬ from classical logic.
◊P = ¬□¬P
Possibly P = Not necessarily not P
For those who are dubious of their browser's character set, □ is indeed meant to display as a box.