Water coming up through the floor may be doing so because the ground water outside the house is higher than the basement floor.
A sump pump is a pump that's located in a recess (sump)in your basement floor. It usually will have some sort of device that automatically switches the pump on when the water collects in the sump. So the pump goes to work before the rest of you floor gets wet. The pump has to have a line that takes the water far enough away from the house that it won't immediately come back in.
Obviously you can't actually lower the level of the ground water, but most of the time the pump can keep ahead of the inflow until the ground water recedes by itself.
You can buy a pump yourself, but I'd recommend finding a good plumber to install one for you. It shouldn't be a huge expense.