God Saves

And they said, "Believe in the Lord Jesus, and you will be saved, you and your household." (Acts 16:31 ESV)
Jesus (יֵשׁוּעַ) means God saves, or more specifically, Yahweh saves. God's salvation is the theme of the Bible.

We are saved by who we believe, not by what we do. God told the people they will be saved if they believe Him. But God revealed His plan of salvation progressively. But at every stage, the underlying theme is always to believe God.

To Seth also a son was born, and he called his name Enosh. At that time people began to call upon the name of the LORD. (Genesis 4:26 ESV)
And Abram believed the LORD, and the LORD counted him as righteous because of his faith. (Genesis 15:6 NLT)
From Adam and Eve, through the antediluvian period till Moses, men thought they were saved by offering animal sacrifices to God.

Now therefore, if you will indeed obey my voice and keep my covenant, you shall be my treasured possession among all peoples, for all the earth is mine; and you shall be to me a kingdom of priests and a holy nation. These are the words that you shall speak to the people of Israel." (Exodus 19:5-6 ESV)
The Law was given to the Israelites through Moses. From the time of Moses till Christ, the Israelites thought that offering animal sacrifices in the Temple was how they were saved.

The old system under the law of Moses was only a shadow, a dim preview of the good things to come, not the good things themselves. The sacrifices under that system were repeated again and again, year after year, but they were never able to provide perfect cleansing for those who came to worship. If they could have provided perfect cleansing, the sacrifices would have stopped, for the worshipers would have been purified once for all time, and their feelings of guilt would have disappeared.
But instead, those sacrifices actually reminded them of their sins year after year. For it is not possible for the blood of bulls and goats to take away sins. That is why, when Christ came into the world, he said to God,
"You did not want animal sacrifices or sin offerings. But you have given me a body to offer.
You were not pleased with burnt offerings or other offerings for sin.
Then I said, 'Look, I have come to do your will, O God - as is written about me in the Scriptures.'"
First, Christ said, "You did not want animal sacrifices or sin offerings or burnt offerings or other offerings for sin, nor were you pleased with them" (though they are required by the law of Moses). Then he said, "Look, I have come to do your will." He cancels the first covenant in order to put the second into effect. For God's will was for us to be made holy by the sacrifice of the body of Jesus Christ, once for all time. (Hebrews 10:1-10 NLT)

For Christ also suffered once for sins, the righteous for the unrighteous, to bring you to God. He was put to death in the body but made alive in the Spirit. (1 Peter 3:18 NIV)

And just as it is appointed for man to die once, and after that comes judgment, so Christ, having been offered once to bear the sins of many, will appear a second time, not to deal with sin but to save those who are eagerly waiting for him. (Hebrews 9:27-28 ESV)

Finally Jesus (יֵשׁוּעַ) came and died for our sins. The revelation of God's salvation is now complete.