Entry door hardware and the weatherstripping can cause a door not to close properly. The entry door hardware includes the door lock, the deadbolt, the hinges and the door strike. Alignment and failed parts can be responsible.
Is something that is attached to the door or the frame, causing it to bind? Requiring you to make an entry door repair. Try to determine what is responsible. Weatherstripping may be too tight. You want it to stop the air, not stop the door from closing. Adjust or replace items as needed if they are binding the door.
You want an entry door to fit snugly, but not so snug that it takes two men and a little boy to get the door closed. Set the weatherstripping so it stops the air and allows the door to open and close. See the article on Weatherstripping for Doors, for more information.
The strike plates on the lock set can cause the door to bind. You can remove the strike plate and use a chisel to remove some wood from the mortise. The plate should be flush with the jamb and not protrude out. Strike plates should not be fastened on top of the jamb. They should be recessed in. See the article on Door Lock Repair, for information on the proper installation of the strike plate.