Best By/Best Before
This is an advisory and not a strict expiration date. It simply means the product will taste best up until that date. It is still edible and okay to eat a little past the listed date, though you may notice a slight change in texture, flavor, or color. For example, chips and crackers often have a “Best By” date. If you eat them after that, they may taste stale. Liquids can start to separate or crystallize, and sugar can clump.
Sell By/Display Until
This terminology is usually found on bread, dairy, and meat. This date helps the store keep track of inventory that needs to be purchased by a certain time. The food is often still good for a little while past the date as long as it is stored correctly. If the “Use By” date is a day or two away, stores will usually discount the product to ensure it sells.
Use By/Expiration Date
Be careful about eating food after this date—it may no longer be safe and could potentially cause illness (check out this article for more information on expiration dates). “Use By” and expiration dates are usually found on refrigerated goods. It's also a good idea to check for a “Use within __ days after opening” stamp on your product.
If you’re in doubt about how long your food will be safe to eat and still taste good, check out sites like StillTasty.com.