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That funny outlet is also called a Ground Fault Circuit Interrupter. It is probably located somewhere close to water; the kitchen sink, the bathroom, outdoors, or the garage.
The outlet is designed to constantly measure the current in the black wire against the current in the white wire. A very small difference between the two wires will cause the outlet to shut off the current very quickly. If you drop the hair dryer into the bathtub, or run over the extension cord with the electric mower, the outlet shuts off.
The buttons are there so you can test the operation of the outlet. Since the outlet is close to water, and has metal moving parts, it is possible that the parts can rust. That is why it is important to test it once a month. Just push the TEST button. The button should pop out and the outlet should shut off. Then push the RESET button to turn the power back on.
If the outlet does not work like it should, you can replace it pretty inexpensively.
Also see the categories Safety, and When Do I Call An Electrician.
One GFCI outlet can protect all the "down stream" outlets and appliances on the circuit. You can test what is protected by pushing the TEST button and seeing what else shuts off. If your GFCI outlet fails when tested, replace it one wire at a time to make sure you wire the new one right. :-)