Today most people think it means He was kind, gentle, and innocent. That He was like a lamb in demeanor.
While that may have been true some of the time, Jesus also taught some hard lessons, rebuked heretics, and physically drove the money changers out of the temple in a fit of righteous fury.
1st Century Sacrifices
In truth, the real meaning of "Lamb of God" is "Sacrifice of God". It means the sacrifice chosen specifically by God. And this would have been obvious to 1st century Jews. Everyone would have understood.
That's because sacrifices were a fact of life in the time of Jesus. The people of Israel had been making offerings and sacrifices to the Lord ever since God established his covenant with Abraham. For centuries, the sacrifices had been well regulated by Mosaic law as documented in the Torah (examples in Exodus, Leviticus, and Numbers). They were important and integral to the culture. That's why we see Joseph and Mary taking Jesus to the temple when he was eight days old to offer a sacrifice. (Luke 2:22-24)
The Paschal Lamb
Further, there was the Passover sacrifice. Passover was the most important celebration on the Jewish calendar. For example, we know the Holy Family traveled to Jerusalem every year to celebrate Passover. (Luke 2:41-51)
During the feast of Passover, the Jews would slaughter a lamb and eat it all. This sacrifice was called the paschal lamb. They could not leave any to waste. They would paint their door frames with the blood of the lamb and sprinkle each other with the blood of the lamb.
All this was done in remembrance of the first Passover during the time of Moses. (Exodus 12) The sacrifice signified the people of God and saved them from God's wrath as he went through Egypt killing the first born of each family.
The Lamb of God
These were cultural norms for 1st century Jews. When people talked about "the lamb", it would have been understood that they were talking about the paschal lamb, the sacrificial lamb from Passover.
And when John the Baptist announced "Behold, the Lamb of God, who takes away the sin of the world," (John 1:29) everyone would have known John was saying this was the sacrifice prepared by God.
Keep pursuing,
Additional Resources
The Need for Context:
As with so much that is written in the Bible, you cannot get the real message if you do not understand the cultural context within which the words were written. Put another way, it is faulty to assume our cultural norms, saying, and definitions apply to works written 2000 years ago.
If you want to understand the Bible, you need to read foot notes, introductions, and supporting materials to get a feel for the intended audience, intent, and message. And if you really want to be on your game, you can begin reading books about the life and times of Old Testament and New Testament Jews and Gentiles.