The Manager is a central component (service?) for looking up stuff, adding Beans, Context, Observers and stuff.
Seam has a Manager too but I think it's a bit more fluffy ;-)
Read the 299 specs and browser the Manager implementation (in both WB and Seam) for an overview
Actually, the Manager in Seam was a conversation manager. The manager of components in Seam was Component. However, it was based on statics and thus not nearly as clean as the Manager design in Web Beans.
The BeanManager API, which is called Manager in the current spec release, is an SPI for use by third-party frameworks like Seam. It's not mean to be called directly by applications.