The term means "old flow" or "old transmission." It refers to arts that were founded before the modern period - pre-Meiji, and there must generally be an unbroken succession since that period.
Aikido is not a koryu as it was founded in the modern period. Daito ryu makes some claims that it is a koryu but these are considered to be sort of cultural/mythological claims; regardless of what sources Takeda drew his skills from he is regarded as so singularly important to the art that he is basically considered to be the founder.
What can be said of Aikido is that it preserves many elements of a koryu structure that did not survive in other gendai arts. The cooperative training structure, lack of competitive focus, and most of three combative suppositions on which it Is technically based derive from koryu bujutsu.
David Hall's Encyclopedia of Japanese Martial Arts has a nice entry on koryu. Available wherever good books are sold.