Caulking concrete cracks is an important but often neglected chore. When concrete is poured, they add expansion joints so that the slab can move as it expands and contracts with temperature changes.
But sometimes concrete still cracks, so score joints, which are shallow grooves cut into the slab, are added to give it a convenient place to crack without marring the surface. Great idea, but if water drains through and gets under the slab it can erode the foundation of the concrete. And, if that water freezes and expands, then the crack expands and multiplies.
So the solution is to fill the crack with a concrete repair caulk, which is flexible but will seal out the water. All you have to do is scrape out the dirt, debris, or weeds, give it a good sweep, then begin filling the gap with concrete repair caulk.