Foreign qualification is the process of registering a company to legally do business in a state other than the one it was originally incorporated in, required once the company has a meaningful physical or business presence there.
A Delaware C-corp headquartered and operating primarily in California, for example, generally has to foreign-qualify in California, registering as an out-of-state ("foreign") corporation doing business there, on top of remaining incorporated in Delaware. Operating without qualifying where required can mean fines, back taxes, and losing the ability to bring a lawsuit in that state until the company registers.
What triggers the requirement varies by state and isn't always obvious. Having employees, an office, or even just a certain volume of sales in a state can be enough, similar in spirit to how sales tax nexus works. Worth checking as a company hires remotely across more states, not just where it was originally formed.
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