Investors buy silver for three reasons: as investment, as hedge against inflation, and for replacement of fiat currency. While many dividend growth investors see no value to holding silver, because it pays no compounding dividend, I believe some precious metal give extra-diversification to any portfolio.
Buying for investment is simply a supply/demand trade on price increase. It's a commodity trade counting on the silver spot to rise. Or, it could be buying silver coin with numismatic value, again hoping for value appreciation.
As an inflation hedge, we can look back to the 1970's when inflation reached 13% and silver prices skyrocketed. During this period, people held silver to offset inflation, and as its price rose investors grew out of the woodwork. Of course, by the 1980's most personally held silver sold off at profit and went into paper investments.
For people who fear paper currency default, we should consider that central governments around the world, including our own Federal Reserve, print money as a solution to stagnant economies. The threat of any countries paper money becoming worthless is real, since none are redeemable in gold or silver as they were at one time.
In 2002, we saw a severe financial meltdown in Argentina and Paraguay when banks closed, only to reopen later, but limiting the amount of money depositors could withdraw. Argentines who converted cash to gold or silver coin were adequately protected during this crisis, while others were not.
Printing money, deficit spending, and endless debt increases has become the norm for leaders both home and worldwide. For no other reasons than these, it's wise to hold some assets in precious metals.