For the reference: https://github.com/hashcat/hashcat/blob/master/docs/hashcat-brain.md
Just a simple example:
you run an attack on some hash (no matter which type 3 or 0):
1. hashcat -m 11300 -a 0 myholywallet.hash some_dictionary.txt -r very_cool_rules.rule
2. it fails, and you decide to make another attack then another and another
3. you execute again attack #1 because you've already forgot about it
4. hashcat brain checks if it already done it in it's database, and if so - rejects all password candidates.
5. You earn the time of not doing the same work twice (or more)