Definitions of Broadway, Off-Broadway and Off-Off-Broadway?

A Broadway theatre is a house of 500 seats or more, used primarily for theatre, and in the district bounded by Sixth Avenue to Eighth Avenue, 41st to 54th Streets. The Vivian Beaumont is outside this district but also qualifies as Broadway. (Madison Square Garden, Radio City Music Hall and City Center all have larger houses than Broadway but theatrical shows in those houses aren't considered Broadway.)
Off Broadway: A theatre of 99 to 499 seats is a reasonable guide for Off-Broadway but the strict definition is about whether the shows are mounted by companies working under an Equity contract or not. (But note: There are some Equity companies working in under-99 seat houses, some of which call themselves Off-Broadway and some of which don't.)
The 99 seat cutoff derives from Equity's showcase code which specifies the conditions under which Equity actors may work for a production not governed by a contract. It limits the length of run (20 or 24 performances), the price which can be charged, and the size of theatre which can be used (a maximum of 99 seats although the Fringe Festival has an exemption).
The theatre festivals and most of the Off-Off-Broadway companies of any note in New York are operating under “showcase code”, and there are hundreds of them. Sooner or later a company gets too big for showcase and must move to a transitional Equity contract. Even if they don't move theatres they are entitled to call themselves Off-Broadway at that point ,and they usually seize the chance because their expenses go up and hence their prices must go up as well.
Source: http://www.talkinbroadway.com