Why did the farmers in the late 1800s want inflation?

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Inflation means that the circulation is running and the production rises as well as the pay. It means that the economic flow is running perfectly.

Farmers wanted more income and revenue, so in order for that to happen, they wanted the production to rise, so that more people could buy from them

Serious deflation issues. Farmers wanted the US to put more money into circulation, causing inflation. Inflation helps farmers in two ways: 1) food costs more, so they get more money for their crops 2) when they have to pay back loans, they do so with inflated money. The money is the same amount, but due to inflation, they have more dollars. (The number of dollars increases, while the actual value of a dollar decreases - it's kind of deep and can be confusing...) 
Farmers also had issues with railroads overcharging them. 

This is why a lot of farmers joined the Populist Party in the early 1890s, since they felt that these were pressing issues and were not being addressed by either the Republicans or the Democrats. Unfortunately for the farmers, the Populists merged with the Dems in 1896 and ran William Jennings Bryan, who lost, and the Populists lost their identity.