The Gauss-Markov theorem is a mathematical theorem that says that in certain cases, the best way to predict something (like a future result) is to find the average of the past observations. It was created by two mathematicians called Carl Friedrich Gauss and Andrey Markov.
Think about it like this: imagine that you want to try to predict how tall your cousin will be when he's an adult. You can find out his height every year since he was five and then use the Gauss-Markov theorem to make a prediction. You would take the average height out of all of the heights you observed over the years and use that to predict how tall your cousin will be when he's an adult.
The Gauss-Markov theorem is a useful tool because it can help make predictions in a way that takes into account all of the data you have available.