As others said, it keeps the smell from the sewer from coming back into your house. Also - that U-shaped bend in the pipes is called a trap.
It prevents sewer gas from coming into your house.Sometimes after a period of nonuse the elbow can become dried out and cause an odor in your house.If this happens just run some water into the sink or bathtub.
First, let's redo that question: Why does the sink have a trap instead of just a straight connection? This usually is what causes clogged drains. The pipe is shaped like that to hold a water seal. It prevent sewer gas from entering the house. Even the toilet has a trap, why do you think water sits in the bottom of the bowl? Since a trap is so accessible there should be no problem getting to it if it gets clogged. Better to clog there than a less accessible place like inside the wall.
Many moons ago, this was called an S trap; today, it's called a P trap, not because it traps pee, but, presumably, because it's P-shaped. Anywho, if plumbing went straight to the sewer with nothing in between, you would be forced to endure the entrance of sewer gases from the sewer--smelly and dangerous. So there is the trap under the sink, where a small amount of water stays trapped in the bend of the pipe, and acts as a barrier between the sewer gases and the air from the trapped water to the pipe going toward the sink. Though it can be a nuisance, it is also nice to be able to retrieve a fallen ring by just removing the trap. So you absolutely need this piece of plumbing.
Do you have a garbage disposal in that sink? The procedure for clearing the clog will be different for sinks with and without garbage disposals. Starting with the basics: Remove as much water as you can from the sink. Seeing as you have put a caustic chemical in the water (Drano) you should be careful and wear gloves. Dispose of this water in the toilet, being very careful not to drip any onto carpets, or floors. Once you have gotten as much water out of the sink as you can, remove everything from under the sink to give you as much room as you can to work. If you have a garbage disposal, look for the outlet connection where the drain pipe connects. This is usually held in place with two screws. Turn the power off to the disposal (for safety). Put a bucket under the disposal and drain pipe. Loosen the screws ans pull the outlet tube loose. You should have some water dripping out. If you have none, the clog is in the disposal drain outlet. Remove the tube and take a screwdriver or other small object and push through the clog. Clean the pipe as well as you can and re-assemble the drain assembly. With no garbage disposal, you just have to remove the trap. Using a pair of channel lock type pliers or a large adjustable wriench, loosen the pipe nut and pull the trap free. Water from the sink will pour out, so again be prepared with a bucket and gloves! Clean the clogs from the trap. Put the assembly back together and you should be ok. If this sounds like something beyond your mechanical skills, call a plumber!
