The New Testament was written in Greek. Some of the doctrine | theology taught in churches conflates ζωή [zoe] (life) with ζάω [zao] (to be alive | to live) in respect of the way certain passages are interpreted.

What did Jesus mean by these words?

In the context of speaking to his disciples about His coming departure from the world, Jesus said:

John 14
  1 Let not your heart be troubled: ye believe in God, believe also in me.
  2 In my Father’s house are many mansions: if it were not so, I would have told you. I go to prepare a place for you.

-- Jesus sat down at the right hand of the Father after He ascended into heaven, and after He had already prepared a place for the ones who believe in Him at the moment He said, "It is finished", when He bowed His head and gave up His spirit (John 19:30) --

John 14
  3 And if I go and prepare a place for you, I will come again, and receive you unto myself; that where I am, there ye may be also.
  4 And whither I go ye know, and the way ye know.

Jesus had begun telling them about His coming departure from the world when He said:

John 13
  33 Little children, yet a little while I am with you. Ye shall seek me: and as I said unto the Jews, Whither I go, ye cannot come; so now I say to you.

Still speaking in the same context, we read in John 14:4 that Jesus also said,
 
"And whither I go ye know, and the way ye know."

Jesus had already told them that wither He goes, they cannot come. Now He tells them that they nevertheless know where He is going, and the way to where He is going - and because it was before He had died, risen again, and before the Holy Spirit had come to the house of God, His disciples were still confused:  

"Thomas saith unto him, Lord, we know not whither thou goest; and how can we know the way?" (John 14:5).

Compare:

(a) As I said unto the Jews, Whither I go, ye cannot come; so now I say to you.

(b) Whither I go ye know, and the way ye know.

(c) Lord, we know not whither thou goest; and how can we know the way?

To Thomas's question, Jesus replied:

"I am the way, the truth, and the life: no man cometh unto the Father, but by me." (John 14:6).

Keep comparing the verses, because further on down in the passage - and still in the same context of speaking to His disciples about His departure - Jesus tells those who believe in Him and belong to Him:

  16 And I will pray the Father, and he shall give you another Comforter, that he may abide with you for ever;
  17 Even the Spirit of truth; whom the world cannot receive, because it seeth him not, neither knoweth him: but ye know him; for he dwelleth with you, and shall be in you.
  18 I will not leave you comfortless: I will come to you.

Take a look at the Greek word used in John 14:2, because the same word is used again further on down in the same passage - but has been translated using a different English word:

John 14
  1 Let not your heart be troubled: ye believe in God, believe also in me.
  2 In my Father’s house are many mansions  [G3438 mone]: if it were not so, I would have told you. I go to prepare a place for you.

G3438: mone. from 3306; a staying, i.e. residence (the act or the place):--abode, mansion.

G3306: meno: a primary verb; to stay (in a given place, state, relation or expectancy):--abide, continue, dwell, endure, be present, remain, stand, tarry (for), X thine own.

John 13
  33 Little children, yet a little while I am with you. Ye shall seek me: and as I said unto the Jews, Whither I go, ye cannot come; so now I say to you.

John 14
  3 And if I go and prepare a place for you, I will come again, and receive you unto myself; that where I am, there ye may be also.
  4 And whither I go ye know, and the way ye know.

"As I said unto the Jews, Whither I go, ye cannot come'; so now I say to you."
"I will come again, and receive you unto myself; that where I am, there ye may be also."

John 14
  19 Yet a little while, and the world seeth me no more; but ye see me: because I live [zao], ye shall live [zao] also.
  20 At that day ye shall know that I am in my Father, and ye in me, and I in you.
  21 He that hath my commandments, and keepeth them, he it is that loveth me: and he that loveth me shall be loved of my Father, and I will love him, and will manifest myself to him.

John 13 (regarding Jesus's commandment):
  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.

John 14
  22 Judas saith unto him, not Iscariot, Lord, how is it that thou wilt manifest thyself unto us, and not unto the world?
  23 Jesus answered and said unto him, If a man love me, he will keep my words: and my Father will love him, and we will come unto him, and make our abode [G3438 mone] with him.

G3438: mone. from 3306; a staying, i.e. residence (the act or the place):--abode, mansion.

G3306: meno: a primary verb; to stay (in a given place, state, relation or expectancy):--abide, continue, dwell, endure, be present, remain, stand, tarry (for), X thine own.

What Jesus was telling them was that THEY were to become His Father's house (in which there are many mansions) - because HE was going to be sending the Holy Spirit down on God's house - and it happened on the Day of Pentecost.

What Jesus had already said was: 

"In my Father’s house are many mansions: if it were not so, I would have told you. I go to prepare a place for you."

"As I said unto the Jews, Whither I go, ye cannot come; so now I say to you."

"And whither I go ye know, and the way ye know." 

"I am the way, the truth, and the life: no man cometh unto the Father, but by me."

"And if I go and prepare a place for you, I will come again, and receive you unto myself; that where I am, there ye may be also.

Jesus is talking about the Temple (house) of God which Christ inhabits, by His Spirit: 

As Paul tells those who BELIEVE Jesus and His words: each one who has the Spirit of Christ dwelling in Him is the Temple (house) of God (Ephesians 2:19-22); and Peter tells us that together we are the living stones who form the one Temple of God (1 Peter 2:5).

Indeed there are many mansions in the house of God, and there is room for each one who believes in Jesus and His gospel 

- and in His Revelation Jesus allowed His apostle John to see what will also be - in a fuller and complete sense following the (bodily) return of Christ and the (bodily) resurrection of the dead in Christ:

"And I heard a great voice out of Heaven saying, Behold, the tabernacle of God is with men, and He will dwell with them, and they will be His people, and God Himself will be with them and be their God." (Revelation 21:3).

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