Not a dumb question at all.
Generally speaking a refractometer is a device that measures he refractive index of a substance. The refractive index is a measure of how much light is bent when it travels from air (or another substance) into the particular substance being measured.
We home brewers use refractometers that are designed to measure the refractive index of sugar solutions. Since that index and the sugar content are related one can determine the sugar content simply by measuring the refractive index. That is done though a scale that is calibrated to the Brix scale. Another property that is strongly related to sugar content is specific gravity and that is measured with a hydrometer. For these devices too the scale can be marked as sugar content (Brix, Balling, or Plato).
Refractometers are not necessarily more precise than hydrometers but they allow sugar content (or specific gravity) measurements on very small samples (few drops) and don’t require cooling a large sample. The sample quickly takes on the temperature of the refractometer which is the temperature that is used in the temperature correction of the reading. This is necessary since the refractive index of a sugar solution also changes with temperature.
I recommend a refractometer only as a supplement to a hydrometer and not as a replacement. Determining the specific gravity of fermented beer is a bit tricky since the alcohol affects the refractive index differently than it affects the specific gravity.
Here is a good BYO article: http://www.byo.com/stories/projects-and-equipment/article/indices/29-equipment/1343-refractometers