A computer relay is a machine or process that receives data and forwards it to another machine or process. Typically, this is a "store and forward" operation, rather than a continuous flow. Data is handled in packets or larger chunks. Also, there is some purpose to having the relay, routing the data from one place to another, performing some operation on the data, etc.
A good example of a relay is found in every email system. Here each relay will store and forward a complete message, after performing some operation needed at that point in the system.