"To make the breakthrough" means to achieve a significant and important success or discovery, especially after a period of difficulty or uncertainty. Full definition
Together, we are focused on making breakthroughs in canine health research to promote dog wellness around the world. (try.embarkvet.com)
To get your boy make a breakthrough with their potty training, give him the new big boy underwear with his favorite superhero or cartoon on it. (toptenstrollers.com)
If that is the case, then today there is news of another app making its breakthrough into the smartwatch market. (androidheadlines.com)