Saves are used if a magic spell or special ability calls for it. For instance the Elemental Connection special ability "Blast" deals [SUM] damage or half on a successful save. So if a player uses this ability against a monster, the GM will roll a d20 on behalf of the monster. If they get the monsters' save value or below the monster only takes half damage.
If you have more questions on P&P and how to play or run TTRPGs, the Perils & Princesses discord is full of helpful people and I'm in there all the time answering questions and just chatting! https://discord.gg/ChtGzqUyzX