For example, assuming a stereo input MP3 file,

ffmpeg -i in.mp3 -filter_complex channelsplit out.mkv

will create an output Matroska file with two audio streams, one containing only the left channel and the other the right channel.

Split a 5.1 WAV file into per-channel files:

ffmpeg -i in.wav -filter_complex
'channelsplit=channel_layout=5.1[FL][FR][FC][LFE][SL][SR]'
-map '[FL]' front_left.wav -map '[FR]' front_right.wav -map '[FC]'
front_center.wav -map '[LFE]' lfe.wav -map '[SL]' side_left.wav -map '[SR]'
side_right.wav

Extract only LFE from a 5.1 WAV file:

ffmpeg -i in.wav -filter_complex 'channelsplit=channel_layout=5.1:channels=LFE[LFE]'
-map '[LFE]' lfe.wav