The basic outline is as follows:

• Inflation, at its base level, is more favorable to borrowers than it is to creditors, because you can pay off a loan in the future with money that is worth less than it was when you took out the loan.
• The most persistent debtors and borrowers in the 19th century tended to be American farmers in the Midwest and South. Until harvests came in and goods could be brought to market, farmers would either have to make do with old stock, or take out credit to purchase goods that could then be paid off after harvests came in. If, however, the harvest was poor or money contracted, they might face economic hardship or ruin. Hence westerners tended to be supporters of free silver, the greenback movement, and the People's Party (Populists).
• Additionally, American miners who specialized in silver tended to support the policy as it would stimulate their industry. The usual terms offered, of a fixed 16-to-1 ration of exchange for silver to gold, would have been much more favorable to silver miners at the time because the market price of gold would have been substantially better than that.
• Creditors, however, like financial establishments of the East, would have preferred very low rates of inflation, so that loans made today would be paid back (with interest) in dollars similar in value. Eastern cities tended to be much more cash rich than rural areas, so credit was far easier to come by.
• The US had recently experienced two major deflationary spirals in 1873 and 1893, which at the time were among the worst economic depressions the US had ever experienced. Farmers lost their holdings, workers lost their jobs, and credit became scarce because people tend to hoard money during deflationary cycles.

To expand on the last point, you hear the word "inflation" and you think of circumstances like Weimar or Zimbabwe. Those are fairly extreme examples. Some inflation, many mainstream economists argue, is likely natural. There is considerable disagreement about how much is natural, desirable, or when government should deliberately pursue inflationary policy (including this so as not to advocate for a particular economic view, which could derail this thread). Small inflationary pressures usually do not present a major problem while the economy and population are growing. The counterpart, deflation, however, is almost always a runaway disaster and was a principal cause of economic woes prior to the end of World War II. As prices fall, businesses cut back on production, and either cut wages or lay off workers. The workers, in turn, lose their spending power, driving demand down further, and continuing the deflationary spiral.

Further reading (for a historical view of Free Silver and history of economic depressions, not necessarily a deep-dive into academic Economics):

Charles Postel, The Populist Vision

HW Brands, American Colossus

Eric Rauchway, The Great Depression: A Very Short Introduction