That's simply how Hungarian does it. "Egy béka" would just refer to any one frog, but "a béka" is the principle of the frog. The froggery itself, what makes a frog a frog. (Or it can refer to just one certain frog.) Maybe think "the species of the frogs".
Hungarian works with principles a lot, and it's a bit hard to grasp if you're unfamiliar with that. A simpler example would be "Itt alma van" - "There are apples here." Or "There is an apple here." With leaving the article out in this example, you do not care about the actual number of the apples, but just about the fact that this space contains apples.