Local reputation is a count of how many trades you've done with a peer at a particular onion address.
The idea is that if a trade with a peer went well, it's reasonable to expect your next trade with that peer to go well too, creating a sort of rudimentary reputation indicator while maintaining anonymity.
As you trade on Bisq, you will see a count appear on the avatars of users you've traded with.
You can reset your local reputation by deleting the
btc_mainnet/tor/hiddenservice folder in your data directory. Bisq will then generate a new onion address the next time it starts, causing you to look like a new trader to all peers on the network.
Do not delete this directory if you have any open offers, trades, or disputes—or you will become unreachable and unable to respond.
See details on restoring your onion address (and thus, your local reputation) here.