What are Doric and Ionian and corinthian?

Doric, Ionian, and Corinthian are the names of the three styles of the capitals on Greek columns. The capital could be loosely called the "tops" of the columns. The Doric style is more or less plain, with just a band running around it. The Ionic style has a wide band that curls under. The Corinthian style is the most elaborate with carved foliage in usually three tiers.