fight,是斗争、打架、战斗的意思,keep fighting就是"继续战斗"、"继续努力"、"继续斗争"的意思.

【例句】
Keep fighting. Don't stop until ALL their base are belong to you.
继续战斗，到所有阵地都属于你之前不要停下。

That's the America I'll keep fighting for every day.
这也是我们每天都将为之奋斗的美国。