tap brakes

Tapping the brakes on a car will slow it slightly.

The author is using a car metaphor, where the speed of the car would be the amount of travel on Labor Day.

So "Americans to tap brakes on Labor Day travel" means that there will be less travel and/or driving on Labor Day.

"tapping brakes' is also a way of showing caution.

So it may mean that people are cautious about traveling on vacation (hesitant, not sure)

Thank you both