Mate guarding is like when you want to keep your favorite toy all to yourself and not let anyone else play with it. Humans sometimes feel the same way about their romantic partners.
When two people are in a relationship, one person might feel worried that someone else might try to steal their partner away. So they might try to keep a close eye on their partner or do things to make sure that their partner only has eyes for them.
This can mean anything from being extra affectionate to getting jealous if someone else talks to your partner. Some people might even go as far as telling their partner what to wear or where to go, so that other people don't get the chance to try and steal them away.
But just like with toys, it's important to remember that people are not objects to be guarded. Trust and communication are very important in relationships, and it's not healthy to try and control your partner's every move. It's important to treat your partner with respect and try to build a relationship based on trust and love.