TWRP is short for Team Win Recovery Project. It is an alternative (not supported by the phone vendor) recovery program available for a lot of phone models, now including the Fairphone 3 (albeit not officially on the TWRP website yet).
The Fairphone 3, much as any other Android phone, has a recovery program installed by default, but this stock recovery program is limited in what it allows you to do.
TWRP opens up more possibilities like easy backup and restore of some things on the phone and perhaps more importantly making installing so-called custom ROMs possible, and then still some more stuff.
Custom ROMs are alternative OSes for a phone. They can be other Android flavours (often built to include as little Google involvement as possible, which many users want) or even totally different OSes.
Please see twrp.me for general information and FAQ.
Running TWRP and custom ROMs has serious implications.
What’s more at the moment, on the Fairphone 3 TWRP and custom ROMs are still in an early stage, trying them out right now is still pioneering stuff and not for the faint of heart.
It can be fun, though, if you have a plan B or backup regarding your phone and your data .