What does John 10:30 mean?

Jesus has been cornered in the temple, in an overtly threatening way, by His religious critics (John 10:22–24). They have challenged Him—dared Him, in effect—to repeat His former claims about being the Messiah. Several months prior, Jesus had given analogies about Himself using shepherding as a theme. Through those statements, Jesus claimed to be the only source of salvation, and that His salvation was eternal, permanent, and irrevocable. When challenged by these men, Jesus repeated those claims, and even expounded on them. In the prior verses, Jesus explicitly said that He offered eternal life, which could never be lost. He first referred to His people as being held in His hand, then referred to the same people as being held in God's hand.

The suggestion carried in that pair of statements is that Jesus and God are identical. Comments along those lines have enraged Jesus' critics in the past (John 5:18; 8:56–59).

Here, faced with an overtly hostile crowd, in tight quarters, with men armed for violence (John 10:31), Jesus connects those dots without the slightest hint of subtlety: "I and the Father are one." Part of the meaning of this statement is lost in translation from Greek to English. Jesus uses the "neuter" form of the Greek word for "one" here, implying that they are "unity." Rather than saying that Jesus and God are the same person, Jesus is claiming that He and God are unified as one, a partial explanation of the Trinity.

Unsurprisingly, this tips the mob's anger over the top, and they start another attempt to assassinate Jesus.