Use a stiff brush to remove loose dirt and debris from the engraved area of your driveway.
Get deep-down debris by going over the engraved area with a shop vac.
Place a tube of asphalt crack repair into your caulking gun. This product can be purchased at any home improvement store.
Squeeze a bead of asphalt crack repair material into the engraved area. Add additional beads -- if necessary -- to fill the gaps.
Push the repair material into the engraved area using a putty knife. Add more repair material if needed.
Smooth the repair material with your putty knife so it's flush with the rest of the concrete driveway. Allow repair material to dry before using that area of the driveway.