If the object is made up of 31 prims or less (including avatar(s) sitting on it). Setting an object physical allows it to be pushed by a resident as a physical object in the real world would be. Physical objects can also be moved horizontally by left-clicking the object and holding down the mouse button while moving the mouse. Holding shift while moving the object will cause it to move vertically, while ctrl-shift will rotate the object.
Other residents can not move an object if Allow anyone to move is not checked in the edit window, except by pushing the object with their avatar.