A BVI (Bridge Group Virtual Interface) is a routed interface that represents a set of interfaces that gets bridged.

So lets say for example that in your router you have two interfaces that needs to get bridged (one wireless and one wired for example) and you want them to behave as if they were part of the same layer two broadcast domain (because you want your hosts in either the wired or wireless interfaces behave as if they were in the same subnet). In this scenario, a BVI would act as the routed interface for that "merged" (really bridged) interfaces.

Any packets that wants to "escape" this merged layer two domain (wired + wireless) will have to go through this BVI.

To this BVI you could assign a layer three address, QoS policies, access-lists or any other "service" you may assign to any physical interface.