Daytime running lights are a system that uses either the headlight bulbs or separate ones to make your car more visible during the day without blinding other drivers. Basically, the system turns on the appropriate lights at about half the normal brightness during the day and then turns them on all the way at night. This is typically controlled with a photosensitive sensor located somewhere on the dash. When the sun is up, or there's enough light landing on the sensor, the headlights are off. When the sun goes down, or you enter a tunnel where there's not much light, the headlights will turn on automatically. Likely, the most common reason this part would need to be replaced is because the sensor is no longer detecting the light levels correctly and is either causing the headlights to never turn on automatically, or it's keeping the headlights on when they shouldn't be. It's probably not difficult to replace the sensor, but it's recommended that a certified mechanic perform the replacement since multiple dash components may need to be uninstalled to get to it.
For most vehicles, the daytime running lights are just an electrical system that leaves on, or dims the headlights during the daytime. However, for some vehicles that typically fall under the luxury category, they have completely separate assemblies that are independent of the headlights that turn on during the day and turn off at night, in lieu of the standard headlights. They are not intended to illuminate the road, so they're not usually as bright.
If you're looking for replacement daytime running light assemblies, or any related parts, take a look at the parts we carry for your vehicle. Car Parts Discount has a selection of daytime running light parts and accessories available for a variety of car and truck models at the lowest possible prices.