See also: Motor casing
A motor mount refers to the tube which a solid rocket motor casing slides directly into. These are usually thick cardboard, phenolic, or composite tubes. Phenolic is preferred for most applications. When the motor slides directly inside the rocket, the rocket is a minimum diameter rocket - referring to the body being as small as possible to fit the motor.
Motor mount tubes are mounted using at least 2 centering rings, and are used as the attachment point for fins for many HPR's. When building an HPR, it is often preferable to extend the motor mount tube 1/4"-1" beyond the final centering ring/thrust ring for ease of attachment and motor retention access. For example, AeroPack motor retention is attached directly to the motor mount tube, and requires ~1/2" of usable tube to bond to.
PICTURE OF MOTOR MOUNT ASSEMBLY W/O OUTER TUBE