When you have a gap between the bottom of your door and the floor, you likely have an air leak that can wreak havoc on your heating and air conditioning bills. There are two possible solutions to this problem.
The first is to adjust your threshold. Most newer thresholds have screws you can adjust to make the whole unit move lower or higher. You’ll want to start by adjusting the screws until the door can open without much drag and there’s no longer a draft.
If you can’t make that work or you have an older threshold without any adjustment screws, then you’ll need to replace the door sweep. These items cost only about $10, but they do require a bit of work; you’ll need to remove the door from its hinges. You’ll want to pop out the hinge pins, set the door on a work surface, then replace the old sweep before putting the door back into place.