Admission in law means that someone has admitted to doing something wrong or illegal. It's like saying "Yes, I did the bad thing I'm being accused of."
Imagine playing with your toys and accidentally breaking a lamp. If your mom asks you if you broke the lamp, and you say "Yes, I did," that's an admission.
In the legal world, admitting to a crime or wrongdoing is taken very seriously because it can be used as evidence against the person in a trial or hearing. It's important to be very careful about what you admit to and to seek the help of a lawyer if you're in trouble with the law.