Under the fractional reserve system we use bank runs are always a threat because banks are inherently leveraged institutions. That is, the law allows them to buy assets (various types of loans, usually) far in excess of their reserves (your deposits). Their aim is to make money out of the difference in what interest rate they pay to depositors and the return on the assets that they buy.

However, in a bank run they need to liquidate assets quickly, but that can be a huge problem because their assets may be illiquid or may be marked down relative to what they will eventually pay out if, for example, interest rates have risen sharply. As such, a run can cause a bank which would be perfectly fine under normal circumstances to suddenly become insolvent.