The range button, found on auto-ranging multimeters that automatically adjust the units of measurement, allows you to set the range manually. An example of this is amps (A) to milliamps (mA) to microamps (μA) and back to amps (A). This is particularly useful when taking measurements close to two ranges, or when taking a number of measurements that could be in either range.
Auto-ranging multimeters are advantageous if you are unsure of the levels you will be testing. For more information, see: Things to consider when using a multimeter!
Another thing worth noting is that some multimeters will have a sleep mode, meaning they will automatically turn off after a period of inactivity before the button is pushed or dial moved. To turn it back on, press the power button or move the dial.