Prime numbers are positive whole number integers, like things you can count with your fingers. However, they have a special property. No other positive integers numbers besides the prime number itself or 1 can be evenly divided by it.
Examples are 2, 3, 5, 7, 11, 13, 17, 19, 23 ...
The number 26, for example, is not prime, since you can divide it by the number 2 and get another integer (26/2 = 13).
9 is not prime, since it can be evenly divided by 3 (9/3=3).
Primes get to be more rare as you go higher up in the numbers. There are an infinite number of prime numbers. The largest one ever found has over 17 million digits. They have a lot of value in pure math research, but also real applications, like better cryptography in computer science.