What was the true purpose of John's baptism? Law or grace?
The baptism John performed in the days prior to Jesus' ministry was a baptism of repentance.
Mark 1:4 John the Baptist appeared in the wilderness preaching a baptism of repentance for the forgiveness of sins.
Mark 1:5 And all the country of Judea was going out to him, and all the people of Jerusalem; and they were being baptized by him in the Jordan River, confessing their sins.
John's baptism was a call in keeping with the words of the prophet Isaiah:
Is. 40:3 A voice is calling,
“ Clear the way for the LORD in the wilderness;
Make smooth in the desert a highway for our God.
According to Isaiah, John's call for repentance within Israel was intended to prepare hearts for the Messiah's arrival. His baptism was a call for repentance unto salvation (i.e., capital "R" as Pastor Armstrong teaches), but forgiveness for sins is made possible only through faith in Christ. Salvation has never been offered through the sacrifices of the OT Law:
Heb. 10:4 For it is impossible for the blood of bulls and goats to take away sins.
No man has ever been forgiven of sins through the sacrifices of the Law. Only faith in God's provision of a Messiah brought forgiveness of sins and salvation. As Paul taught:
Rom. 3:19 Now we know that whatever the Law says, it speaks to those who are under the Law, so that every mouth may be closed and all the world may become accountable to God;
Rom. 3:20 because by the works of the Law no flesh will be justified in His sight; for through the Law comes the knowledge of sin.
Rom. 3:21 But now apart from the Law the righteousness of God has been manifested, being witnessed by the Law and the Prophets,
Rom. 3:22 even the righteousness of God through faith in Jesus Christ for all those who believe; for there is no distinction;
Therefore, those who came to John in the wilderness for baptism were receiving forgiveness of sins because they were trusting in God's promise of a Messiah. They received water baptism as a sign of their repentance and their faith in God's promised Anointed One. Their faith saved them, not their baptism.
Today, men and women are saved in the same way. We have faith in God's Anointed One, Jesus Christ, our Messiah, and because of our faith we receive water baptism to symbolize our repentance hearts and our new life through faith in Christ.
How did the people in John's day understand these things? In the same way we understand them today: by studying God's word. The Jewish scriptures (i.e., the OT) testifies to the sin of every man, the requirement for repentance, the need to appeal for God's mercy and forgiveness, and the atonement God would provide through the Messiah. In John's day, the promise of a Messiah had yet to be fulfilled, while in our day, the promise has been fulfilled. In both cases, however, faith in God's provision was the means of forgiveness and salvation.
Even John himself was an OT saint saved by his faith in the coming Messiah, and when Jesus began his ministry, John sought to confirm the Messiah's arrival:
Luke 7:18 The disciples of John reported to him about all these things.
Luke 7:19 Summoning two of his disciples, John sent them to the Lord, saying, “Are You the Expected One, or do we look for someone else?”
Luke 7:20 When the men came to Him, they said, “John the Baptist has sent us to You, to ask, ‘Are You the Expected One, or do we look for someone else?’”
Luke 7:21 At that very time He cured many people of diseases and afflictions and evil spirits; and He gave sight to many who were blind.
Luke 7:22 And He answered and said to them, “Go and report to John what you have seen and heard: the BLIND RECEIVE SIGHT, the lame walk, the lepers are cleansed, and the deaf hear, the dead are raised up, the POOR HAVE THE GOSPEL PREACHED TO THEM.
So those who responded to John's call of repentance were those who had faith in God's promise, and they wished to demonstrate their faith by receiving the baptism John offered.