Your garage door is supposed to last a long time and weather all sorts of, well, weather. So spotting damage at the bottom of the door isn't pleasant, especially as that damage might make the gap between the door and ground bigger and allow cold or hot air in -- not to mention pests. You've got to figure out how the damage formed so that you can stop more from forming, and then you have to repair the damage to the door.
Improper Closing Force and Weak Springs
Your garage door shouldn't close too quickly. Even if it isn't slamming onto the ground, if it's closing with force, there may be something wrong with the springs. The springs should help lower the door gently, and if the springs are too weak, either because they're damaged themselves, worn out, or were improperly installed, they aren't going to be able to restrain the weight of the door. The result is the door closing with too much force, and that can damage the bottom of the door because it's hitting the ground too hard.
You may also want to look at the force adjustment of the door. This is an adjustable feature that helps you fine-tune the door's ability to reopen if it senses something under the door that shouldn't be there.
Debris on the Ground
If the door is closing with too much force and not reopening the second it detects something under the door, then whatever is under the door can damage it. Think rocks, twigs, and other items that aren't big enough to really force the door to reverse course but that aren't soft enough to crush down when the door hits. It's difficult to prevent leaves from blowing into the path of the door, especially if you have a stop behind the door that prevents leaves from scooting under the door and into the garage on windy days. You'll have to increase the number of times you sweep the area to try to control the debris that ends up in the path of the door.
Misalignment in the Tracks
If the door is misaligned even slightly, then one corner of the door may land right before the other -- causing damage to that first corner if the door isn't set to reopen immediately. Take a look at the tracks and see if you can spot any issues; this could also be due to a problem with one spring but not the other.
Other than sweeping around the door more often, these issues usually call for professional repair. You really don't want to do anything with the springs or tracks, other than cleaning, if you don't normally work on garage doors. The weight of the door and the potential for a spring to break make this part of your house one of those that will benefit more from the help of a garage door repair specialist.