Law was basically a system of merit. Blessing was conditioned on man's performance. It blesses the deserving. Law says: "Do this and live." Law makes demands but does not supply the power. Law goes together with meritorious works and self-effort.
Grace, on the other hand, is based on the undeserved favor of God in Christ Jesus. Man does not work in order to be blessed but works through love because he is blessed. It blesses the undeserving. Grace says: "Believe and live. And now that you are alive do this." Grace beseeches and then gives the power to do it. Grace goes together with reliance and faith.
Law kills and condemns. Grace makes alive and justifies. Law says: "Love your neighbor as yourself." Grace says: "Love your neighbor as I have loved you."
There are many other differences but this should suffice.
