Let's take a look at John chapter 10 in the original language. Here is a PDF of John 10 in Greek with interlineal English.
John 10:30 is written:
ΕΓω καί ό πατΗρ εν εσμεν
Ego kai ho pater en esmen
I and the father one are.
The final word, "εσμεν" (esmen) is a plural conjugation, as compared with "εστιν" (estin) would be the singular. This may be an indication that the sense in which Jesus meant this statement relates to the preceding context. In the 10:28, Jesus states that no man shall remove His sheep from His hand. In 10:29, Jesus states that His Father gave the sheep to Him, and no man is able to snatch them from His Father's hand. Thus, 10:30 may indicate that Jesus and His Father are united in abilities and purpose.
In 10:31-10:33, Jesus' audience begins to stone him for blasphemy, accusing him of claiming to be God.
In 10:34 and 10:35, Jesus responds to his their assertion that he is blaspheming by calling himself God. He responds that scripture calls gods all of those unto whom His Word was given.
In 10:36, Jesus says, "...you are saying that you are blaspheming that I said, 'The Son of God I am.'"
Finally, in 10:38, Jesus says, "...and you should be believing: that in Me the Father, and I in Him."
In the context of the discussion Jesus is having with his audience, he says that all the people who have been given the Word are gods, that Jesus is the Son of God, that Jesus and the Father are in each other, that Jesus has some of the powers of the Father, that the goals of Jesus and the Father are one.
This is consistent with other statements by Jesus, for example, John 6:38, "That down I am stepping out of the heaven, that not I may be doing the will of Me, but the will of the One sending Me."
In considering what Jesus meant in the quote of John 10:30 and why God would cause us to receive this particular wording, it seems that Jesus and God are telling us that Jesus and the Father are effectively the same thing from the perspective of the judgment which will be applied to the humans. This is consistent with John 14:6, "... I am the way and the truth and the life; no one is coming to the Father if not through Me."
In this sense, John 10:27-10:30 seems to mean something similar to: There is one flock, which God gave to Jesus. No man shall remove a sheep from Their flock. Together they are one Shepherd of the sheep.