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四海為家 literally reads, “Four Seas Serve-As [my/one's] Home.”
Together, 四海 which literally means “four seas” is understood to mean “the whole world” or “the seven seas.” It's presumed to be an ancient word from back when only four seas were known - so it equates to the modern English term, “seven seas.”
This can be translated or understood in a few different ways:
To regard the four corners of the world all as home.
To feel at home anywhere.
To roam about unconstrained.
To consider the entire country, or the world, to be one's own.