Okay kiddo, so let's say your teacher asked you to write a story about what you did over the weekend. You could make things up and say you went on a trip to the moon, or you could tell the truth about going to the park with your family.
Now, if you tell the truth, we say you have integrity. It means you're honest and you do the right thing even when nobody is looking.
So when someone gives testimony of integrity, it means they're telling the truth and they're sticking to their values even if it's hard or nobody else agrees with them. It's a really important quality to have, and it helps people trust you and believe in what you say.