The idea behind bracing is to restrict the muscle from expanding. In this way there is less force or stress put on the muscle fibers. No one has really proven or disproved bracing as an effective treatment for tennis elbow.
A brace gives your elbow, forearm, and wrist support during everyday activities. It also limits the pain during daily activities. The idea is to give the arm a rest while it heals but still allow you to do what you need to do on a day-to-day basis.
The brace should be worn throughout the day at all times. It can be taken off at night. Give it about four to six weeks to allow time for the microdamage at the elbow to heal. If you aren't healed or at least better, then a short-course of physical therapy may be needed.