Open-source means that the source code is available for anyone to read. (It's also closely connected to copyleft licenses, which explicitly allow copying and derivative works, but they aren't quite the same.) It's generally very good for security software to be open-source, because it means anyone can see how it works and highlight security flaws, and it makes it much harder for malicious code (i.e. a password manager that sends all your passwords to the creator) to sneak in under the radar.