Hollywood - District in Los Angeles in USA and it is famous for movie studios and celebrities, and Hollywood is now synonymous with Cinema of USA. Hence the name Hollywood.
Bollywood - It is used with Hindi Cinema based in Bombay mostly, often even Indian Cinema is referred to as Bollywood in international circles. The term is a derivative of Bombay and Hollywood.
Tollywood - It is used with Telugu Cinema now a days, but it is used even with Bengali cinema too. Technically Tollywood should refer to Bengali film industry as Bengali Cinema is based in Tolly Gunj, a place in Kolkata and hence the name - Tollywood. But since Telugu cinema is now popular and even it adopted the name Tollywood.