Reducing is a term that shows up in a lot of recipes, and apparently you're just supposed to know what it means - whether you've cooked much or not.
Really, it just means to evaporate a portion of the liquid; in your case, dry white wine, but it could be any liquid - wine, stock, sauce, etc. Often you'll see a direction to reduce a sauce by some fraction, perhaps a half, so using your best judgment, you evaporate and evaporate until only half the original volume is left.
that point, you can refer to it as "a reduction," and all of your mother's friends will think you're quite a cook.
Reducing a liquid makes it thicker and intensifies the flavor.
Pans, which are wider at the top, such as a saucier, provide lots of surface area for water molecules to evaporate, and so are useful for reducing the time it takes you to reduce your liquid. Using a high-quality (i.e. heavy-bottomed) pan will also allow you to turn up the heat with less risk of burning your food, which also reduces the reducing time.