Does imperturbable refer to something you can't break through?

You're probably mixing up imperturbable with a similar word, impenetrable. Impenetrable means difficult or impossible to move beyond, which can be a physical barrier or something more conceptual. Switch up a few letters, and you get an entirely different meaning with imperturbable: calm, cool, and collected in behavior; not easily upset or bothered.

In the novel Bleak House, Charles Dickens describes chief legal counsel Mr. Tulkinghorn:

His imperturbable face has been as inexpressive as his rusty clothes. One could not even say he has been thinking all this while. He has shown neither patience nor impatience, nor attention nor abstraction. He has shown nothing but his shell.

And from Sinclair Lewis's Babbitt:

The lights of the hotel and the cottages became yellow dots, a cluster of glow-worms at the base of Sachem Mountain. Larger and ever more imperturbable was the mountain in the star-filtered darkness, and the lake a limitless pavement of black marble.