Low voltage dropout regulator.
The LM2937-5 is a 5V regulator that can supply 500mA. The LM2937 differs from the common 7805 by having a much lower dropout voltage, 0.5V vs. 2.0V. Very nice if your 9V battery dips due to a large current draw.
NOTE: The output capacitor is critical to maintaining regulator stability. Without one, you will not measure 5V at the output. The output capacitor must be at least 10µF. Please see page 7 of the datasheet for further information.