Tennis elbow is caused by overuse. Any activity that strains the muscles around the elbow over and over again can cause it. There’s also a version golfers get called “golfer’s elbow.”
In tennis, hitting a backhand puts some stress on your forearm muscles, which repeatedly contract when you hit the ball. If you have poor technique or grip the racquet too tightly, that stress may increase in the tendons that connect the forearm muscles to the elbow. The tendons may get small tears.