The Greek word, pronounced okh-los, that is usually translated into English as "multitudes," actually means a crowd of common people, in contrast to the "upper classes" of society, political and religious. For the most part, it was the "common people," the "oppressed masses," who were the followers of Christ. They were looking for a leader who would liberate them from the lives that they were living.
Although the purpose of the first coming of Jesus Christ was to not be recognized by most of humanity (see When Will You Be Judged?), "great multitudes followed Him" during His ministry. And, "a great multitude with swords and staves, from the chief priests and elders of the people" were responsible for His becoming the Lamb of God. Ironically, those who followed Him would have prevented His becoming the Savior because for the most part they followed Him for political reasons e.g even after years of being taught by Christ, Peter fought to defend Christ's life (see Their Eyes Opened After Christ's Tomb Did).
"great multitudes followed Him"
Christ's famous "sermon on the mount" was delivered to the "humble" people of that society, physically and psychologically.
"And seeing the multitudes, He went up into a mountain: and when He was set, His disciples came unto Him: And He opened His mouth, and taught them, saying,
Blessed are the poor in spirit: for theirs is the kingdom of heaven.
Blessed are they that mourn: for they shall be comforted.
Blessed are the meek: for they shall inherit the earth.
Blessed are they which do hunger and thirst after righteousness: for they shall be filled.
Blessed are the merciful: for they shall obtain mercy.
Blessed are the pure in heart: for they shall see God.
Blessed are the peacemakers: for they shall be called the children of God.
Blessed are they which are persecuted for righteousness' sake: for theirs is the kingdom of heaven" (Matthew 5:1-10 KJV)
Christ's miracles were seen by them, but they didn't realize that the miracles were about a future Kingdom of God in which there would be no hunger or sickness.
"As they went out, behold, they brought to Him a dumb man possessed with a devil. And when the devil was cast out, the dumb spake: and the multitudes marvelled, saying, It was never so seen in Israel.
But the Pharisees said, He casteth out devils through the prince of the devils.
And Jesus went about all the cities and villages, teaching in their synagogues, and preaching the gospel of the kingdom, and healing every sickness and every disease among the people. But when He saw the multitudes, He was moved with compassion on them, because they fainted, and were scattered abroad, as sheep having no shepherd. Then saith He unto His disciples, The harvest truly is plenteous, but the labourers are few; Pray ye therefore the Lord of the harvest, that he will send forth labourers into his harvest" (Matthew 9:32-38 KJV)
Most (but certainly not all) of the people of the multitudes that followed Him were deliberately Gentiles (i.e. He "charged them that they should not make Him known"), as prophesied by Isaiah ("Esaias" in the King James).
"Then the Pharisees went out, and held a council against Him, how they might destroy Him.
But when Jesus knew it, He withdrew Himself from thence: and great multitudes followed Him, and He healed them all; And charged them that they should not make Him known: That it might be fulfilled which was spoken by Esaias the prophet, saying,
Behold my servant, whom I have chosen; my beloved, in whom my soul is well pleased: I will put my spirit upon him, and he shall show judgment to the Gentiles. He shall not strive, nor cry; neither shall any man hear his voice in the streets. A bruised reed shall he not break, and smoking flax shall he not quench, till he send forth judgment unto victory. And in his name shall the Gentiles trust." (Matthew 12:14-21 KJV)
Ironically, it was the multitudes that rejected Him and had Him crucified that were responsible for making Him the Lamb of God. Notice here that Peter, because even he didn't yet understand, tried to prevent Christ's sacrifice as The Lamb of God.
"And while He yet spake, lo, Judas, one of the twelve, came, and with him a great multitude with swords and staves, from the chief priests and elders of the people. Now he that betrayed Him gave them a sign, saying, Whomsoever I shall kiss, that same is He: hold him fast. And forthwith he came to Jesus, and said, Hail, master; and kissed Him.
And Jesus said unto him, Friend, wherefore art thou come?
Then came they, and laid hands on Jesus, and took Him. And, behold, one of them which were with Jesus stretched out his hand, and drew his sword, and struck a servant of the high priest's, and smote off his ear.
Then said Jesus unto him, Put up again thy sword into his place: for all they that take the sword shall perish with the sword. Thinkest thou that I cannot now pray to My Father, and He shall presently give Me more than twelve legions of angels? But how then shall the Scriptures be fulfilled, that thus it must be?
In that same hour said Jesus to the multitudes, Are ye come out as against a thief with swords and staves for to take Me? I sat daily with you teaching in the Temple, and ye laid no hold on Me. But all this was done, that the Scriptures of the prophets might be fulfilled. Then all the disciples forsook Him, and fled." (Matthew 26:47-56 KJV)
Fact Finder: In what ways will multitudes of people be gathered to Christ upon and after His return?
See Spiritual and Physical Gatherings