The physgun is one of two primary tools of Garry's Mod, along with the tool gun. It is similar to Half-Life 2's gravity gun in that it is capable of manipulating objects using the Source engine's physics. It differs from the gravity gun in that there are no limits in what it is capable of manipulating except for the size of your penis. The physgun originated from the beta leak of HL2, and was a cut weapon.
The physgun can pick up any entity in Garry's Mod, dependant on individual server's settings. For example, certain servers may employ prop protection, which prevents you from moving other player's props, even though normally this is possible. The physgun is also capable of rotating objects and moving them closer or farther away from yourself (by holding down your use key). The physgun can also 'freeze' objects, which prevents them from moving at all until unfrozen.
It's pretty much like cats eating people-food.