With few places for rain water to go, it often times takes the easiest route of running down your foundation walls to the soil beneath your basement.
There it pools, and as the groundwater level rises around you, your sump pump is the final line of defense against a flooded basement. If the water is rising too fast, your pump may not be able to pump it out fast enough. If the power goes out or your pump burns out, the water rises into your home.
If you have a nicely finished basement, you've got a costly problem on your hands. Standard insurance policies don't cover sump pump failure or flooding, so if you have to tear out the drywall and carpeting, hire a water mitigation company to dry it out and prevent mold growth, and replace all water damaged possessions, walls, and flooring, you may find yourself paying $10,000 out of pocket.
The smarter choice is to install a battery backup sump pump with a raised float. Having the float raised higher than your primary sump pump ensures it doesn't turn on during normal circumstances. If the water rises above the primary pump because it can't keep up, the secondary pump will kick in. If the power goes out and the water rises above the primary pump, the secondary pump kicks in then as well.
This way you're preventing your primary pump from being overworked during heavy flash floods or snow melt, and you've also got a pump capable of running on battery if the power goes out.
If you need a new primary pump as well, consider getting a combination sump pump system that comes with the primary pump, the secondary pump, and the battery.