What causes my cement garage floor to become damp?

The reason your cement garage floor can become damp is that it wasn’t prepared correctly, and there is ground water underneath the floor that is getting through the vapor barrier that should have been installed when the floor was first laid. To repair this problem, you will have to either remove the problem section of the garage floor and refinish it with better drainage and leaching gravel, as well as better builder's sand, or you will have to remove the entire floor and rebuild it correctly, ensuring this time that the proper drainage and leaching gravel is in place and that a good vapor liner is used before you pour the cement.