What does this scripture mean in relation to convential Christianity? What Law is this?

At the time it was written it referred to Mosaic Law. But in a more general sense it simply means God's Law.

Jesus magnified and revealed the intent of the Law, showing that the spiritual application of the Law takes precedence over the literal, though the literal should not be negated. Anyone claiming to be a believer, but does not do what God wants him or her to do makes their prayers an abomination unto Him.

Jesus fulfilled the old law by walking in perfect love all the way to the cross and love was the fulfillment of the old law ten commandments, and Jesus ushered in a new covenant where your sins and lawless acts I will remember no more and where these have been taken away there is no longer any sacarfice for sin (Hebrews 10:16-18) read all the Hebrews scriptures very inlighting.