The minimum frame size is indeed 64 bytes (14-byte header plus 46-byte data area plus 4-byte CRC). Historically the reason for a minimum legal frame size was to ensure that the collision detection mechanisms that are at the heart of Ethernet can operate correctly. This is easier to grasp if you think of Ethernet as a shared bus made out of a single long coaxial cable with stations tapped off it at intervals as in the days of old. The same basic mechanisms apply to point-to-point twisted pair, it's just harder to visualise.
Frame length is also one of several criteria used to decide whether a recieved frame is valid or not. Where a short frame is concerned, the length differentiates between a legal frame and a fragment. At the other end of the scale, a frame longer than the maximum allowed is not a valid frame but a jabber
