one's native land; one's homeland
A somewhat literary or formal term for one's home country, often used with a nostalgic or patriotic tone.
彼は故国を離れて十年になる。
It has been ten years since he left his homeland.
It has been ten years since he left his homeland for work.
I fondly recall the culture of my native land.
When the war ended, many soldiers returned to their homeland.
Even far away, I always think fondly of my homeland.
母国 is a warm, everyday term for one's mother country, whereas 故国 is more formal and evokes distance or separation from home.
異国 means a foreign land, the opposite of 故国, one's own native country.
故郷 refers to one's hometown or home region, while 故国 refers to one's entire home country, so the two differ in scope despite both meaning 'home'.
Compound of 故 (former, old) and 国 (country). The exact historical derivation is uncertain, but the combination naturally yields the meaning 'old country' or 'homeland'.