The mussels use these threads to cling to rocks and rope. We humans are looking into uses for us.
There is an extensive article on the subject, but to sum it up here are some great applications:
1) A biodegradable glue to stick human tissue together.
2) Generate universal hemoglobin compatible with all blood types.
3) Create a membrane that separates water from oil (for oil spills for example)
4) Generate an underwater glue.
5) Combine the glue properties with the membrane properties to collect, for example oil, on the hull of a boat painted with the byssus glue.
And on!
Read more on:
https://www.researchgate.net/publication/334379884_Mussel-Inspired_Surface_Engineering_for_Water-Remediation_Materials