Your company may be a foreign company. Where your company, for example, has operations or makes sales, outside of its home jurisdiction it may be required to register as a foreign corporation in those other jurisdictions.
The most common situation I encounter is a federally (Canada) incorporated company operating in any Canadian province or territory. While federal incorporation involves listing the company’s head office, the company is still required to register extra provincially where it is doing business. For example, a federal corporation with a head office in BC would register extra provincially in B.C.
On the U.S. side, the same applies to a Delaware corporation that has a head offices in another state, for example California, and requiring the company to register as a foreign corporation in that other state. As such, all Delaware incorporated startups based in California are (or should be!) registered foreign corporations in California.
Each jurisdiction has different rules defining when your company has to register as a foreign corporation. A head office is only one way to be considered a foreign corporation. As a founder, it’s less important to understand the exact requirements (that’s the lawyers job) than to understand that doing business in jurisdictions outside of where you are incorporated may require the company to register as a foreign corporation.