Well, farm gate value is all about how much money farmers make from selling the crops and animals they produce. You know how farmers grow things like corn and carrots and they raise chickens and cows for milk and meat? Well, those things are sold to companies and stores who then sell them to us to eat.
When farmers sell their crops and animals to these companies, they get paid a certain amount of money. That money is called the farm gate value. It's called that because it's the value of what comes out of the farm gate - the place where the crops and animals leave the farm.
The farm gate value is important because it helps farmers know how much they're making for their hard work. It can also help governments and organizations figure out how much money is being made in the agricultural industry in a certain area.
So, farm gate value is just a fancy way of saying how much money farmers make from selling the things they grow and raise.