Tokyo Babylon is about Subaru Sumeragi, an onmyouji (usually translated to "medium") who uses his skills to help people. He has an older twin sister (Hokuto) and his best friend is Seishirou Sakurazuka.
While there are individual stories featured in each manga, the main story that weaves itself into the story is how the Sumeragi clan and Sakurazukamori clan are mortal enemies, yet Subaru and Seishirou are close friends. Seishirou claims that they met not long ago while Subaru was chasing a bird shikigami (a spiritual bird) and tripped. However, Subaru keeps having strange dreams about meeting Seishirou long ago. So how will it end? I'm not going to spoil it for you. Tokyo Babylon is a prequel to X, so if you've seen X you probably have a good idea of what happened. Unfortunately, X always depresses me because I find it too angsty, and I like the more carefree nature that Hokuto brings to Tokyo Babylon. For a more complete summary, you can visit Rabi's Tokyo Babylon Page.