Some Cisco devices only support changing MTU globally, others support changing MTU per interface.
As MTU is tied to the media, and the standards that support the media, the only time you commonly want to change MTU is for Ethernet interfaces that support MTU larger than the Ethernet standard of 1500 bytes.
There are several reasons for wanting a larger MTU than Ethernet's 1500. Network devices, especially software based routers, "spend" a similar amount of work forwarding a frame/packet, regardless of its size. Larger frames/packets may allow more payload to be forwarded in the same amount of time. Additionally, frames and packets often have a fixed amount of overhead per frame and/or packet, so larger frames and packets allow more "payload" to be transferred using the same amount of bandwidth. Lastly, other media types, then Ethernet, often support MTU larger than Ethernet's, so if there's Ethernet in the path, you cannot leverage the other media's MTU capability.
At L2, normally you want the sender and receiver to support the same MTU. If the receiver only supports a MTU smaller than the sender's, the receiver will drop the received frame/packet.
At L3, IP will fragment packets that are larger than the MTU the media supports, but this should be avoided.
