Mortification of the flesh is a really big and hard word to understand, so let's try to break it down.
Have you ever heard of the phrase "no pain, no gain?" Mortification of the flesh is kind of like that. It's when someone purposely does things that make their body uncomfortable or painful, in order to become closer to their religion or beliefs.
For example, think of how sometimes your parents or teachers might ask you to do something hard, like getting up early in the morning to go to school or practicing a tough math problem. Even if it's not fun or easy, you do it because you know it will help you in the long run.
Similarly, some people believe that doing painful or uncomfortable things, like fasting (not eating at all or eating very little), wearing uncomfortable clothing or shoes, or even hurting themselves (like whipping themselves or sleeping on a hard floor) can help them become closer to their religion or god. It's kind of like a way of saying "I'm willing to put myself through this tough stuff because I believe in something bigger than myself."
But it's important to know that not everyone believes in doing this kind of thing, and some people think it's not necessary or even harmful. It's up to each person to decide what they believe and what they feel comfortable doing.