Weatherstripping your door is extremely important for energy conservation and your comfort. If you can see daylight around your door, then outdoor air is entering your house and mixing with your conditioned air. This means your air conditioning/heating equipment must work longer and more often to maintain the indoor temperature.
Can you imagine how much air would enter your house if every door were like this?
It would all add up to a sizeable hole in your house. A few dollars in weatherstripping can prevent this.
Bare bones weatherstripping is the peel & stick type that just sticks to a surface. It comes in different densities and compresses easily or firmly. It also comes in different widths. I would only use this as a last resort as it doesn’t seem to want to stick very well.
Modern doors have a kerf that allows you to install a vinyl coated weatherstripping. You can simply pull the old strip out and push the new one in. The vinyl has a small barb that pushes into the kerf and holds. This needs to be cut when you come to a corner, and then you start the next strip. When you’ve done the perimeter of the door, check to see that the sweep on the bottom of the door is in good condition. You may be able to adjust the sweep, if not just replace it.
The big test is whether or not you can see daylight anywhere around the door when you close it. If you do can’t see daylight, your job is done.