Silver is, and was, cheaper and more abundant than gold, which "backed" the US Dollar at the time. This gold standard meant that the supply of money in the economy was kept relatively fixed, since either more gold would have to be mined or the conversion ratio between gold and dollars would have to be changed in order to print more money. The fixed supply, along with an increasing demand for money, raised the price of money in the real economy -- deflation.

Deflation is bad, really bad. In particular, it's bad for debtors. Their loan contract probably specifies that you have to pay $100 over the next five years, but all of the sudden, those $100 are now worth $102 in contract-date dollars (nominally it's still 100, but in real terms it's more), it's going to be harder for you to pay.

Farmers in the American West and Midwest were often debtors in this period, while the new class of wealthier northeastern businessmen were often creditors. Thus, the creditors liked the deflation, since their contracts were worth more, and the debtors hated it, since theirs were worth less. This was reflected in politics: the creditors supported the Republican platform of William McKinley on 1896 (obviously this debate goes back further than this, as do the policies that lead to this point, but 1896 is an important year in the currency debate and the most remembered). This platform involved staying on the deflationary gold standard. The debtors supported William Jennings Bryan, a Democrat, who supported bimetallism, the policy of using both gold and the more abundant, cheaper, silver to back the Dollar. This would be inflationary, as the Dollar would be worth less because there was a silver boom, dropping prices of silver and, thus, the Dollar if a bimetallic standard was in place. This is what Bryan referred to in his famous "Cross of Gold" speech at that year's democratic convention. He believed that by keeping America on a gold standard, moneyed interests were harming the farm class that he represented.