break through
To finally push past something that was blocking you.
To break through means to force your way past something blocking your path, whether it's a physical barrier or an obstacle of a different kind. When firefighters break through a locked door to rescue someone, or when tree roots break through concrete, something that was stuck or blocked suddenly gets past the obstacle.
The phrase often describes moments when persistent effort finally succeeds. A scientist might work for years before breaking through with a discovery that solves a problem. A basketball team trailing by ten points might break through the other team's defense and start scoring. When you've struggled with long division for weeks and suddenly it clicks, you've had a breakthrough (which becomes one word when used as a noun).
The phrase carries a sense of force and determination. Breaking through isn't easy or gentle: it requires pushing hard against resistance. When sunlight breaks through storm clouds, when a shy student breaks through their nervousness to give a great presentation, or when doctors break through to a new treatment, something powerful overcomes something stubborn.
You might hear people say they're trying to break through to someone who won't listen, meaning they're working hard to get that person to finally understand. The phrase suggests that moment when effort, persistence, or force finally wins against whatever stood in the way.