Product attributes are quantifiable or descriptive aspects of a product (such as, color). For example, if you were to create an attribute for color, with the values of blue, green, yellow, and so on, you may want to apply this attribute to shirts, which you sell in various colors (you can adjust a price or weight for any of existing attribute values).
You can add attribute for your product using existing list of attributes, or if you need to create a new one go to Catalog > Attributes > Product attributes. Please notice that if you want to manage inventory by product attributes (e.g. 5 green shirts and 3 blue ones), then ensure that "Inventory method" is set to "Track inventory by product attributes".