It's used in modal logic, where it was invented, to define relations between models and constructions of new models from old models, which are used to show that different classes of model have the same discriminatory power for modal theories. Van Bentham's introduction of bisimulation was in his PhD thesis, 1976, Modal Correspondence Theory.

There'a quite a bit in Blackburn, de Rijke & Venema (2001) Modal Logic on bisimulation; section 2.2 explains the basics of the application to modal logic.

It's used in modal logic, where it was invented, and is used to define relations between models and constructions of new models from old models, which are used to show that different classes of model have the same discriminatory power for modal theories. Van Benthem's introduction of bisimulation was in his PhD thesis, 1976, Modal Correspondence Theory.

There'a quite a bit in Blackburn, de Rijke & Venema (2001) Modal Logic on bisimulation; section 2.2 explains the basics of the application to modal logic.