An exterior threshold takes a lot of abuse from foot traffic and weather—and it can only withstand so much. If your threshold is in rough shape, replace it.
Thresholds come in wood and metal, both of which come with a rubber gasket for sealing out the cold. Most exterior thresholds also have a sill beneath them. If the threshold is rotted, the sill probably is too. The sill is beveled on one side to drain water away from the house. It fits tightly between wall studs and under the jambs and casing, so it has to be cut before it can be removed.
You may also want to replace an interior threshold because the old one is ugly or because new flooring on one side of the doorway calls for it. An interior threshold simply rests on the floor with no sill under it.
Installing a new threshold and sill will take between two and three hours. Protect your floors with a drop cloth before you begin, and make sure you're comfortable with basic carpentry skills.