Imagine a person who lives in a big house with lots of land around it. This person likes to spend time taking care of the land and planting things in the ground like vegetables or even raising animals like cows, pigs, or chickens.
This person doesn't do it to make money or as a job, but more as a hobby or a way of life. They are called a "gentleman farmer" because they are like a rich gentleman (even if they're not rich!) who likes to take care of their farm.
So, a gentleman farmer is someone who lives on a big piece of land and grows things or raises animals, but they don't do it as a job, they do it for fun!