MME stands for MultiMedia Extension. MME drivers are audio drivers meeting the microsoft MME specification. Wikipedia has this to say about MME drivers.
The Multimedia Extensions were released in autumn 1991 to support sound cards , as well as CD-ROM drives, which were then becoming increasingly available. The Multimedia Extensions were released to Original Equipment Manufacturers (OEMs), mainly CD-ROM drive and sound card manufacturers, and added basic multimedia support for audio input and output and a CD audio player application to Windows 3.0. The Multimedia Extensions' new features were not available in Windows 3.0 real mode. Windows 3.1x would later incorporate many of its features. Microsoft developed the Windows Sound System sound card specification to complement these extensions. The MME API was the first universal and standardized Windows audio API. Wave sound events played in Windows (up to Windows XP) and MIDI I/O use MME. The devices listed in the Multimedia/Sounds and Audio control panel applet represent the MME API of the sound card driver. MME lacks channel mixing, so only one audio stream can be rendered at a time. MME supports sharing the audio device for playback between multiple applications starting with Windows XP, up to two channels of recording, 16-bit audio bit depth and sampling rates of up to 44.1 kHz with all the audio being mixed and sampled to 44.1 kHz.