A certificate (also referred to as a cert) is a tradable and stackable item equivalent in value to five of the equivalent non-stackable item. Certificates can be converted into their equivalent items (and vice-versa) for free by various non-player characters (referred to as "certers"). Only certain commonly-traded items can be converted.
Many players prefer to trade with certificates in order to complete the trading process easier and faster, though it takes a significant amount of time to trade the items for certificates and vice versa. Only 12 non-stackable items can be added per trade screen, but 25,769,803,764 stackable items can be added per trade screen (assuming that each 12 are a different item and the player doing the trading is very, very rich).