To "beat" the traffic means to leave earlier than most people so that you can avoid travelling when the roads are crowded. You can try to beat the traffic:

• on your morning commute
• when driving home from a road trip on a holiday weekend
• when leaving a large event like a baseball game

This phrase uses the word "beat" in the same way that it's used in sports, so you can imagine "beating the traffic" as running a race against all the other cars on the road.