What does it mean by the balance of power in western civilization in the year 1660-1789?

That could mean a lot of things, that's quite a large chunk of history there.

However, the most obvious answer would be something to do with the English Restoration in 1660 and either the election of George Washington or the start of the French Revolution in 1789.

Those are probably the most significant events affect balance of power on those dates in western civilization.