"The farmer gained insight into the way of overcoming the long fallow period in the farm"
The meaning of this sentence is that the farmer was able to understand the source of the problem in the farm, which will help him to find an effective solution to fight against this problem. The word "fallow" is used to refer to an unsuccessful period of time or, in other words, a period of time in which nothing good is produced. Furthermore, the word "insight" refers to a sudden understanding of a specific problem.