The phrase "to catch a breath" means to take a short break or pause in order to rest and regain your breath after physical exertion or when feeling overwhelmed. Full definition
When you are on this bike, you might have to stop for catching your breath after 30 minutes of using it. (aimworkout.com)
The rest periods that are used are only 10 to 20 second breaks, so the trainee can catch their breath before starting another exercise. (fitnessandpower.com)
The kid's pool was so cold that our child couldn't catch his breath in it and the large pool was too deep to be able to move about comfortably with him. (havebabywilltravel.com)