Peter's sermon in Acts 3 was after the lame man was healed. The lame man was brought to the temple gate, but could not enter the temple because he was unable to walk. The lame man is a good illustration of those under the Law. The Law brought people close to God, but could not bring them into the presence of God because of the people's inability to walk in righteousness.
The Law was intended to be applied in the heart. Keeping the Law was not a matter of obeying a set of commands.
We should not make Christianity a set of commands to be kept. This leads to dryness in the Christian life.
Keeping the Law is honoring God and as a result holding God's Law in high regard. The psalmists spoke of keeping God's law in spite of not being able to obey all the commands therein. To keep the Law was to love it because of honoring God. This would lead the Jews to look for the Saviour which God promised.
In the same way, keeping the Lord's commands is loving His commands because we love Him.