Подавать is imperfective. Подать and Подавать are a pair. And дать(per)+давать(imp) are a pair. По creates a new pair, with a new meaning in this case. The wikipedia page explains all the meanings of verbs, and gives their counterparts, and gives other prefixed forms related to the verb youre looking at. Prefixes don't always change the meaning in a 100% clear way, sometimes theyre just used to create a sort of word "descendant". For instance издать (из meaning "out from", "out of"), "give out from" doesn't exactly paint an obvious picture of what it means: to publish. Just look at that link for the actual meaning of подать/подавать.

A whole lot of verbs (though certainly not all) come in a pair that is exactly the same except for the last 3 letters. Imperfective ending in ать and conjugating аю аешь ает аем and so on, while the perfective ending in ить and conjugating ишь ит им ите, and the я form having a consonant mutation, like ответить --> отвечу
Sometimes a syllable is added дать + ва = давать .
Prefixes can make an imperfective verb into its perfective counterpart, or the other way around. купить (perf) --> покупать (imp) (the ить also changes to a ать) Buying usually happens once, so the imperfective word for "to buy", is sort of the secondary, prefixed word.