They were drawn to Him seeking healing, and to see miracles take place, and hear Him because of the power that comes with His word. The word always comes with power.
What percent of the crowd gathered around Jesus because He was the Savior, the Son of God, and they were there to have their sins forgiven, to believe the Gospel, and seeking eternal life? I would say that percentage was very low. There is a difference between loving Jesus because of His sacrifice for us, and seeking Him for what we can get out of Him. One motivation is spiritual, one is worldly. I would say those who were amazed at his supernatural acts did not relate them as a sign He was the Savior, but a curiosity or amazement sort of like we would view a magic act. The others were interested in an earthly king to restore the independence of Israel and stop Roman tyranny.
What was the primary purpose Jesus healed? It was that we might believe. I am sure He had compassion on those suffering, but His purpose here was not to amaze people with supernatural acts, or to take business away from the doctors, or to change the government. His kingdom, as He said many times, is not of this earth. These were signs that pointed to Him as the Savior and Messiah.
The Lord was kind and patient to almost all He encountered despite our lack of understanding. In fact, the only two groups I can recall the Lord getting visibly angry at was the Phariees who should have known better, but were the greatest hypocrites of all. The other group was the money changers trying to make a buck off thehouse of God. They Lord did not even get angry at his Roman executors. In fact, did not one of the Roman soldiers confess Jesus?
More important than why the crowds followed Him back then is why do they follow Him now? After all, back then, while Jesus was on earth, there was no New Testement. We have no excuse. The Gospel is in print, media, video, etc, and is proclaimed every week at least once. What draws us now? Is it a love for the Lord because of what He did for us, a Savior that is worthy of our worship and praise? Or, do we follow Him to have our names on a church roll for whatever reason, a free pot luck, a social club, gossip center, to please our spouse? Are we involved in a ministry for some reason other than love for the Lord, like maybe working our way to heaven? This gets back to the thread of the relation between works and faith.
I cannot be too harsh on the early church crowd, as for all their faults, they did not have the knowledge of the Gospel we do today. And certainly, they took many more risks to their lives for expressing their faith in Christ than we do in America today.
In some ways humanity has not changed from 2000+ years ago. Without a relationship with Jesus, if we bother to seek Him, it is out of some selfish reason. Back then, it might have been the amazement of an act of Jesus, today it might be to get out of a fix we got outselves into.
The bottom line is that praise and worship goes to Jesus Christ. We trust Him to guide us through life, make us more like Him, get us through the rough times, and bring us to glory. Jesus Christ is not an insurance policy, a quick fix, or a magician. He is God.