The Index of Refraction
The index of refraction is the ratio of the speed of light in a vacuum relative to the speed of light in the material. This doesn't sound very useful, but there's one other implication of the index of refraction: light traveling through a material will bend through an angle dependent on its index of refraction. Water has a different index of refraction than mineral oil, for example, but in addition, water with no sugar has a different index than water with 10 percent sugar mixed in, which has an index different from 20 percent sugar water. A refractometer lets you easily measure the index, but to ensure an accurate reading, you need to calibrate the device with refractometer standards.
Refractometers
There are many different refractometers, but the general principle for all of them is the same. Light is sent through a small volume of liquid, then it goes through a prism, then through an adjustable scale that displays the index of refraction or an equivalent number. The light sent through the refractometer is bent differently depending upon the index of refraction of the material in the sample volume. The measured angle also depends on all sorts of other things, such as temperature and humidity. To compensate for those sorts of parameters, you calibrate with a refractometer standard.
Refractometer Standards
A refractometer standard is a liquid whose index is known to a very high degree of accuracy. For example, a refractometer standard from the National Institute of Standards and Technology (NIST) has an index of refraction 1.46945 plus or minus 0.00006. The index varies with temperature as well: for every degree Celsius over 20 degrees, the index will decrease by 0.00037. So if the temperature was 28 degrees C, you would clean out the refractometer sample volume, insert a few drops into the chamber, close the refractometer, and set the scale to read 1.46649. Chances are the device will not allow you to adjust to closer than 1.4665.
Brix Standards
There are a special class of refractometer standards called brix standards. Brix is a fancy name for the percentage of sugar contained in a water solution. The index of refraction of a sugar water solution varies with brix, so a refractometer can be used in applications from soft drinks to syrup. Again, the numbers can't be trusted without doing a calibration. Brix standards are precise mixtures of sugar and distilled water. Refractometers specifically designed to measure brix are best calibrated with these brix standards, even though they can't be traced to NIST standards.