Elastic thread is thicker than normal thread and it stretches more. Elastic thread is used with stretchy fabrics and materials like jersey cotton and elastic.
In many cases, a zigzag or stretch stitch with regular thread will provide enough give to work with stretchy materials, but elastic thread can be used for certain cases. See How to Sew Stretch Fabric for tips on working with stretchy fabrics.
Elastic thread is used in the bobbin in combination with regular thread in the top stitch because the elastic thread is too thick to be threaded through the machine. Note that the amount of stretch is limited by the regular thread.
Elastic thread is only used in the bobbin and not as a top stitch. If you use it as a top stitch, the thread will snap and possibly damage your machine. The thread is also too thick to properly thread through the sewing machine.