Attack Damage (AD) is your physical damage statistic, and Ability Power (AP) is your magic damage statistic :) Some champions can pick and choose which they build and adjust their playstyle accordingly, but if you hover an ability you'll either see orange numbers next to an axe symbol, or purple numbers next to a magic blast symbol to see which stat that ability scales with.

For example, with Kog'Maw, if you build AD items on him you'll primarily be auto attacking to hurt enemies, and using his abilities to augment his auto attacking power and positioning. But if you build AP items, you'll be focusing on hitting people with recasts of your ultimate ability, using abilities to stave off enemies who get too close and largely ignoring your auto attacks.