In the Bible it talks of Jesus being one with the Father John 10:30 but also says that we should be one with them John 17:11. In the Bible's original Greek text, is the same word used for both, or is the word that describes our oneness with them different? The scriptures that speak of our heavenly Father and Jesus as being one are often used to prove the doctrine of the Trinity. (The Trinity being of one nature and one substance.) Does the original Greek word denote a physical oneness in substance, or a oneness in unity, purpose, action, and nature?
Working in unison, living in unity.
Mark 10:8 8
and the two will become ·one body [as though they were one person; T one flesh; Gen. 2:24]’. So they are no longer two, but one.
16 I have other sheep that are not in this ·flock [fold; pen; C a reference to future Gentile followers of Christ], and I must bring them also. They will listen to my voice, and there will be one flock and one shepherd.
30 The Father and I are one.”
Judges 20:11 (ASV)
11 So all the men of Israel were gathered against the city, knit together as one man.
Oneness usually implies oneness of mind, actions, and so forth.
1 Corinthians 1:10 (In contrast to modern setting.)
10 But I urge and entreat you, brethren, by the name of our Lord Jesus Christ, that all of you be in perfect harmony and full agreement in what you say, and that there be no dissensions or factions or divisions among you, but that you be perfectly united in your common understanding and in your opinions and judgments.
Colossians 3:13-14 (Note relationship between love and unity (oneness))
14 And above all these [put on] love and enfold yourselves with the bond of perfectness [which binds everything together completely in ideal harmony].
In a deeper sense, just as a Husband and Wife are ONE through a God-ordained arrangement, the Christ is ONE with the congregation. This principle is especially important, because its necessary in saving through unity:
1st Corinthians 7:14 (Note the saving aspect of oneness)
14 For the unbelieving husband is sanctified in the wife, and the unbelieving wife is sanctified in the brother: else were your children unclean; but now are they holy.
In this way the congregation (Christ's bride, loved as his own body) is also cleansed by the Christ due to marital contract and attains everlasting life.
Conversely, the "Harlot" separating, disuniting from the Christ, unifying with Satan's world, becomes one with the world, and they share sins all the way back to Abel's murder. Luke 11:51, Revelation 17:2 COMPARE TO: 1 Corinthians 6:16
From the contents of your question I am assuming you are making reference to:
John 17:22 KJV
And the glory which thou gavest me I have given them; that they may be one, even as we are one:
Very often in order to understand the meaning of any particular Scripture it is necessary to take into account many other Scriptures, and that is true in this case. This verse must be read along with not only what is said in chapter 17, but has to reach back to what the whole situation was at the time and especially what Jesus was conveying to his disciples.
In order to take in the whole concept we have to start with:
John 13:1 KJV
Now before the feast of the Passover, when Jesus knew that his hour was come that he should depart out of this world unto the Father, having loved his own which were in the world, he loved them unto the end.
Beginning here Jesus is telling them not only what is going to happen, not only in the immediate future, but giving them encouragement for the persecution to come.
He begins by showing them how important humility is by washing their feet, and gives more emphasis to it when:
John 13:6, 7 and 8 KJV
6 Then cometh he to Simon Peter: and Peter saith unto him, Lord, dost thou wash my feet?
7 Jesus answered and said unto him, What I do thou knowest not now; but thou shalt know hereafter.
8 Peter saith unto him, Thou shalt never wash my feet. Jesus answered him, If I wash thee not, thou hast no part with me.
So what does humility have to do with oneness?
Matthew 20:28 KJV
Even as the Son of man came not to be ministered unto, but to minister, and to give his life a ransom for many.
Here Jesus is telling them; that in order to be like him, they have to give up self and serve others.
John 13:14 KJV
If I then, your Lord and Master, have washed your feet; ye also ought to wash one another's feet.
He goes on further to say:
John 13:16 KJV
Verily, verily, I say unto you, The servant is not greater than his lord; neither he that is sent greater than he that sent him.
And again you wonder what does that have to do with oneness. well just hang on I'll get there.
John 5:19 KJV
Then answered Jesus and said unto them, Verily, verily, I say unto you, The Son can do nothing of himself, but what he seeth the Father do: for what things soever he doeth, these also doeth the Son likewise.
Here Jesus is telling them that he does not arbitrarily do things, that the father is a part of everything he does, and that they are patterned after the ways of the father.
John 13:34 and 35 KJV
34 A new commandment I give unto you, That ye love one another; as I have loved you, that ye also love one another.
35 By this shall all men know that ye are my disciples, if ye have love one to another.
The purpose of this command is pretty self evident in that in order to represent Jesus they must assume the characteristics of Jesus.
John 14:10 and 11 KJV
10 Believest thou not that I am in the Father, and the Father in me? the words that I speak unto you I speak not of myself: but the Father that dwelleth in me, he doeth the works.
11 Believe me that I am in the Father, and the Father in me: or else believe me for the very works' sake.
Here Jesus is saying in effect by now you should know by now, after seeing all my miracles; that the father and I are part of the same God, but if you don't believe me you at least ought to believe it because of the miracles.
John 14:19 and 20 KJV
19 Yet a little while, and the world seeth me no more; but ye see me: because I live, ye shall live also.
20 At that day ye shall know that I am in my Father, and ye in me, and I in you.
Here Jesus is telling them that once he goes to the Cross and ascends to the father, that he will again be spiritually united with the father, and that his spirit will be united with them, so that they all become a common spirituality.
From this point up until chapter 17 he warns them of the travail about to beset them, and so that they will not be blindsided and lose faith. And in the first part of chapter 17 he is in effect telling them that after he has gone to the cross and ascended that he will give them a new eternal life.
John 17:1 and 2 KJV
1 These words spake Jesus, and lifted up his eyes to heaven, and said, Father, the hour is come; glorify thy Son, that thy Son also may glorify thee:
2 As thou hast given him power over all flesh, that he should give eternal life to as many as thou hast given him.
Finally we get to your Scripture:
John 17:21 and 22 KJV
21 That they all may be one; as thou, Father, art in me, and I in thee, that they also may be one in us: that the world may believe that thou hast sent me.
22 And the glory which thou gavest me I have given them; that they may be one, even as we are one:
So to answer your question what Jesus apparently meant when he said "be one" was he was referencing being one Spirit for eternity.