Let's look at some of the original language that was used here so we can better understand what this verse means. The word "salvation" comes from the Greek root word of sōtēria (σωτηρία). As it was used in the original language, it means "deliverance and preservation" and can therefore imply rescue in a worldly/physical context like from enemies. Or, as we also see, it can be used to suggest an eternal/spiritual rescue. 

"I give them eternal life, and they will never perish, and no one will snatch them out of my hand." - John 10:28 ESV

In the verse previous (Acts 4:11), Peter calls the Sanhedrin the "builders" who are responsible for the Jewish people and thereby the proper observance of the Jewish religion. This word, "builders," means that the elders, priests, and scribes of the Jewish religion should have recognized Jesus. There are many places in their Scripture, which is our Old Testament, that provide incredibly specific descriptions that clearly identify Jesus as the Messiah that they have been (and still are) waiting for.

For example, in the last week of His life alone, He fulfilled prophecies of the donkey He rode into Jerusalem on (Zechariah 9:9; Mark 11:1-7), the way the Roman guards cast lots for His clothing (Psalm 22:18; Mark 15:24), and the fact that His bones were not broken (Psalm 22:17; John 19:31-37).

It's unbelievably unfortunate and sad that the Jews had a long history of ignoring, abusing, and executing their prophets (1 Kings 19:10; 2 Chronicles 36:16; Jeremiah 2:30). Because of this, they missed the coming of the One they had been waiting for - He who is the only One who could bring them salvation.

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