The cutoff option sets the bandwidth of the encoder – bandwidth meaning the highest frequency that will be encoded.
While typically you wouldn't restrict the bandwidth when encoding audio for home theater, music listening, etc., there are other use cases such as telephony or video conferencing, where it is not necessary to transmit the whole frequency spectrum.
For example, the primary frequencies of speech are situated well below 8 kHz, so you can cut off the higher frequencies and save required transmission bandwidth. This was also done in the early days of telephony to be able to share a line among multiple users.
Various encoders support this option, such as:
Especially AAC and Opus are interesting because they were created with low bit rate or narrow band transmissions in mind.