If there is someone at work or at school or even at a place where you go to socialize, that acts mean and snarky towards you (seemingly for no reason) you have several choices. You can attempt to talk to the person civilly and try to find out why they are being mean to you, or you can simply ignore them and hope that the person gets bored/tired of treating you that way, or you can be “brought down to their level” by responding in a way that is mean and snarky towards that person, essentially making you not much better than they are.
Basically, it means doing something bad/naughty/mean/rude because it’s easier (for any number of reasons) than doing the right thing or taking the high road.
Another example would be a young impressionable person, who ends up taking drugs or shoplifting, so he/she will fit in with a particular crowd. Maybe because they want to appear to be cool, or they’re afraid that they won’t be popular, or that they’re concerned that other people might view them as not being independent of their parent’s rules.
Another example is a person who goes out and cheats on their SO, because their SO cheated on them first. It’s like they’re trying to teach the other person a lesson, or to one-up the original cheater, or to make the other person feel guilty, or to make his or herself feel desirable despite being cheated upon. So in fact, they’ve been “brought down to the level” of the original cheater.