Attributes provide a mechanism for easily applying a set of criteria to items in your database. You can then easily compare the values within the attribute set between items. For example, suppose you are searching for a car to buy. You could create an attribute set with fields for color, model, cost, year, condition etc and apply this set to each item you find in your search. You could then easily compare the values between candidates. Another powerful feature is the ability to select the value of an attribute from all assigned values, and search for all items with that value assigned. For additional information on this feature see the advanced search help page.
An attribute can be used in multiple sets. For example, the color attribute could be used to describe the car above and also be applied in a different set when comparing gloves.