Many things may render a car door unable to close properly, including a stiff, swollen or damaged gasket; a broken latch mechanism; or one or more loose door hinges causing the door to hang unevenly. Dirt, sticks and other debris may also be stopping the door from closing.
A common cause of a car door not closing is a seized or broken door latch clasp. Locate the latch clasp on the interior edge of the car door that meets the frame of the vehicle, and ensure the latch is in a lifted, open position. If the latch clasp is closed, gently attempt to lift the latch manually using a screwdriver. The latch should spring back into the open position. If the latch does not stay open, it may be necessary to replace it.
New door gaskets may be stiff and require a little bit of wear before a car door shuts properly and without much effort. If a door gasket is torn or partially detached, it may prevent the door from shutting. Inspect the gasket for damage and replace if necessary, or apply adhesive to the rear of a detached gasket and attach the gasket to the inner door frame.
A door hanging from a loose hinge may need tightening in order to close properly and could cause additional damage. Locate the hinges for the door in question, and ensure that the door is properly hung.