Okay kiddo, so you know how when people do math equations they have to follow certain rules to make sure their answers are right? Unitarity gauge is kind of like a rule for physicists when they're working with particles called "gauge bosons" which are like the force carriers for things like electricity and magnetism.
It's a way for them to make sure that their calculations follow this rule called "unitarity" which means that the sum of the squared probabilities of all the possible outcomes of a particle interaction should always add up to 1.
Basically, unitarity gauge is a method that makes sure that the calculations for these gauge bosons are sensible and accurate, so that we can learn more about how they interact and impact things like the world around us. It might sound complicated, but it's really just a way to make sure that physicists are doing their math right!