Sometimes fridges (the classic type that have a freezer at the top) exhibit a mode of failure whereby ice and water appears in the refrigerator, but there is no apparent frost buildup in the freezer (the defroster cycle is working).
A possible cause for this is that the defroster drainage has iced up (plugged up with ice) and so when the defroster comes on to melt frost, the water is not escaping, but pooling up below the evaporator (the "labyrinth" of fine piping through which the refrigerant flows, which which removes heat from the freezer).
As the water pools up, it also freezes, so it builds up layer by layer. This is hidden behind the paneling in the freezer, so you don't see it. Eventually it builds up to the point that the water starts to drip through the air aperture between the freezer and fridge, and that's when you start seeing water and ice in the fridge compartment.
The air aperture is what cools the fridge: it allows cold air from the freezer to drop down into the lower compartment. On some fridges, one of the temperature control dials in fact just adjusts the size of this aperture.
To attack the problem, empty the freezer and remove the bottom and rear paneling to gain access to the true floor of the compartment and the evaporator. Chip away all the ice from the bottom, being careful not to damage the evaporator or bend its delicate fins (often very thin aluminum). Use a hair dryer to melt ice in the tray below the evaporator. Find the drainage hole and unclog it by removing ice by whatever means possible. (I've used a soldering iron to help speed up the process, for instance: it's hot, and shaped right to poke into the iced-up drain hole.) One option is to just unplug the fridge and wait, of course, but with these aggressive steps, you can get the fridge back in operation quickly, before your food spoils.
Now if you simply de-ice the unit, it the problem may come back, as happened to me: the problem recurred within just a few months of the first time I did the above procedure.
So, the second time around, I added an additional step: I took a piece of solid copper wire, some 2-3 mm thick, wrapped a few turns of it around the defroster heating element , then routed the other end of the wire an inch or two into the defroster drain hole in the collection tray below. This wire is permanently installed like this, and its job is to pick up some heat from the defroster and conduct it down the drain hole during the defrost cycle. This configuration prevents the drain from icing up.
Since I did this, the fridge has been trouble-free for several years: no water at the bottom, no chunks of ice.