M4A refers to mp4 files that contain only audio data.
iTunes and Apple's iPod have made this format popular. Your M4A files are encoded exclusively in either the lossy AAC or the lossless Apple Lossless.
In general, M4A files can also contain audio data encoded with other compression methods. However, this is rare.
The contents of the file may also be protected by DRM (Digital Rights Management). Then you need a corresponding, possibly paid license to view the content.
Most audio players can play this format.
MP3 and MP4 hardware player only in exceptional cases.