Media Transfer Protocol
A standard for transferring media files between two connected devices. Typically, the files are audio (or similar) files and the connection is USB.
A typical use would be transferring music to and from a phone over a USB cable.
Unlike some other protocols, MTP is designed to allow multiple devices to access the same set of files at the same time, without the risk of files becoming damaged.
For example, consider song files stored on a phone's internal memory, and that phone connected to a computer. With a protocol such as USB Mass Storage, the portion of internal memory with the songs must be disconnected (in software) from the phone before the computer can access that memory to add or remove songs. Otherwise files could be damaged if both devices attempt to change them at the same time. It isn't possible to disconnect that internal memory if the phone has one pool of internal memory that also stores the software that keeps the phone running (as some phones do.)
MTP solves that problem by carefully managing the connection and access to files, ensuring that files aren't damaged. The drawback is that MTP isn't as widely supported. Also, MTP only allows simple access to specific types of files, whereas other protocols allow access to more files in more parts of memory.
MTP is almost identical to PTP, a related protocol for pictures.
MTP was created by Microsoft, but has since been adopted as an (optional) part of the USB standard.