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.
From this document:
When you configure and enable routing
on the BVI, packets that come in on a
routed interface, which are destined
for a host on a segment in a bridge
group, are routed to the BVI. From the
BVI, the packet is forwarded to the
bridging engine, which forwards it
through a bridged interface. This is
forwarded based on the destination MAC
address. Similarly, packets that come
in on a bridged interface, but are
destined for a host on a routed
network, first go to the BVI. Next,
the BVI forwards the packets to the
routing engine before it sends them
out of the routed interface.
I really hopes this helps you understand BVIs.