Can anybody help me understand what this really means, "to speak after the manner of men"?
You really should provide some context for this. I take it that it is from the King James Version of Galatians 3:15: Brethren, I speak after the manner of men; Though it be but a man's covenant, yet if it be confirmed, no man disannulleth, or addeth thereto.
One literal translation has it as: Brethren, as a man I say it, even of man a confirmed covenant no one doth make void or doth add to
In modern English:
Brothers, I speak as a man when I say that even if it is only a man's covenant, it is one that is confirmed and that has nothing added or taken away from it.