They can compress the asphalt beyond its design, breaking the bond, and leaving cracks. The ultimate goal in asphalt pavement maintenance is to protect the surface from the elements and to prevent water from infiltrating through cracks into the base. Nearly everything that contacts asphalt is bad for it. Vehicles can cause compression damage from overloading Car tires can, especially on turns, scrub away the finer aggregates from the pavement surface leaving a rough texture and a weaker pavement. Oil and fuel spills, which are petroleum products like the asphalt cement, can soak into and soften the pavements so the aggregate isn't bound together as good as it was originally.
Water can cause damage several ways.
Water penetrating the pavement through cracks can cause damage in both warm and cold weather. In warm weather it soaks down into and softens the base under the pavement. Since asphalt is flexible, vehicle traffic will cause it to move up and down over the soft base and pump out the base. This creates a void under the pavement and allows it to fail under the weight of the vehicles on top. In cold weather you have the same expansion and contraction scenario plus the freeze - thaw action that can create the void under the pavement without the need for vehicles on top.