Okay, so the classic classification we all learned in school, that separates animals in Kingdom, Phylum, Class, Order, Family, Genus and Species, was created by a guy called Linneaus.

Now, back in Linneaus' time, they didn't know about evolution, much less genetics, so he tried to classify animals based on the physical similarities he could see. All animals with scales in the same group (reptiles), all animals who lactate in the same group (mammals), all animals with feathers in the same group (birds), and so on and so forth.

Nowadays, though, we can use genetics to determine more precisely how related different species of animals are to eachother, and so comes a new classification, that puts animals that evolved from the same ancestor together in the same group. Which is the cladistic classification

Now a lot of animals did fit more or less with the linnean classification, but a lot of them don't. A lot of animals we thought were related are actually very distant genetically and only look similar due to convergent evolution, and a lot of the ones we thought had nothing to do with eachother turned out to be be really closely related.

Birds and reptiles are one such case. Both birds and the animals we more commonly consider as reptiles, are descended from the same ancestor and are currently considered part of the class Reptilia, which are all diapsids, meaning they have two openings on each side of the skull. Not only that, birds are descendants of a now extinct group of theropod dinosaurs called Archaeopteryx, which makes them living, breathing dinosaurs!