The best way to explain the difference between slotted and drilled rotors is to explain all the possible rotor configurations: "Smooth," "Slotted," "Cross-drilled," and "Drilled and Slotted."
Smooth brake rotors (which may be "solid" or "vented") have a perfectly smooth surface. When a brake pad touches the surface of a smooth rotor, the wear of the pad is minimized compared to a slotted or drilled rotor. While the lack of grooves and/or drill holes has some negatives (smooth rotors can get hotter and are more likely to have contaminated surfaces), they're the ideal choice for a typical daily driven vehicle. They maximize brake pad life, they resist cracking and rust, they tend to last the longest of any rotor design, and yet they're still extremely capable in everyday situations.
If smooth rotors have a problem, it's that many of the cheapest rotors are not manufactured to the correct specifications. If a rotor is too thick or too thin - or even slightly out of round - it can cause all sorts of problems for the braking system (and your wallet). So, for that reason, we always recommend buying the best quality smooth rotor available. Even the nicest smooth rotors are cost comparable to OEM replacement rotors, but usually offer better wear and performance than a cheap OE replacement.
Slotted rotors have long grooves in a spiral pattern that serve two purposes. First, the slots channel any dust or contamination on the rotor or pad surface away from the rotor and into the air. The grooves basically make sure the pad and rotor surface stay as clean as possible.
The slots or "grooves" have another purpose too - cooling. The slots increase the surface area of the rotor, and also have a small impact on the airflow over the rotor surface. Both of these benefits are small, but it's fair to say that a slotted rotor has better heat dissipation than a smooth rotor, all else being equal.
Cross-drilled rotors have holes drilled thru them from the face to the back, the purpose of which is to keep rotors cool. Cross-drilled rotors have a much, much larger surface area than any smooth or slotted rotor, and tend to dissipate heat better than any other rotor design. This leads to better performance, especially in track or towing situations where brake fade is a big concern. Cross-drilled rotors also look cool, and many people say they perform better in wet conditions than a smooth or slotted rotor.
The increased cooling ability of cross-drilled rotors comes at a cost, however: Cross-drilled rotors are more expensive to replace than smooth rotors, tend to wear out more quickly than smooth rotors, and also tend to "chew up" brake pads more quickly than smooth rotors. For this reason, cross-drilled rotors are usually only found on performance vehicles. Still, whatever kind of vehicle you have, cross-drilled rotors (or drilled and slotted rotors) are the way to go if you're looking for maximum performance.
Drilled and Sloted rotors combine the benefits of slotted rotors (good clean contact surface) and cross-drilled rotors (great cooling) for maximum performance benefits. If a smooth rotor is the boring but reliable "Toyota" of the rotor world, then drilled and slotted rotors are the "Ferrari" or "Porsche" of the rotor world - exotic performance at a relatively exotic price. But if your primary concern is performance, go with drilled and slotted.