In the context of BDSM, a serving tray is a small tray which is strapped to a slave so that they can serve drinks or other small items. The design of the tray means that the slave's hands are not needed to support the tray and are often bound behind their back. Serving trays have a strong forniphilia element to them in that they objectify the wearer, reducing them to a tool rather than a person.
Needless to say, serving trays are not used for their practicality. Indeed, it is not uncommon to combine their use with additional restraints and impediments such as high heels, leg irons, and other bondage devices to make movement (and thus control of the tray) as difficult as possible. This will make it more likely that the slave will spill or drop something, giving the master or mistress the excuse to discipline them.
Serving trays can be bought from a number of on-line retailers.