A fridge usually has a drain that leads out to the bottom in order to collect condensation. Your drain may be clogged, which is not too unusual. If your veg drawer is at the bottom of the fridge, take it out and look for a small opening at the base of the fridge; push a pipe cleaner or something similar through the hole and see if the water starts to drain. Of course, there are many different fridge designs and I am just giving general advice. A little more info about the fridge will probably allow one of the guys here to give you more specific advice.
Learn something every day