Your Basement Could Be Leaking For Many Reasons...
...But Hydrostatic Pressure Is Most Likely The Issue
Don't be scared by the term "hydrostatic pressure" -- it just means water ("hydro") that has no where to go ("static"), so it forces ("pressure") its way into your basement. When the soil around your home's foundation becomes oversaturated, the water table (the point at which the underground soil/material is entirely saturated) rises and creates this hydrostatic pressure.
An elevated water table most often occurs during/after heavy rainfalls, which is why most homeowners notice more leaks during those events.
There could be other reasons for your basement leaks including -- but not limited to -- floor cracks, cove joint leaks, window well issues, poured concrete cracks and basement wall seepage, among others.
This is why it's important to let an experienced, local basement waterproofing company evaluate your particular basement leaking issues so you can make sure you install the correct solution the first time.