Some have used the above passage to argue on the deity of Jesus because He claimed that the Father is greater than Him. 

How does this fit in with the understanding of the Trinity?

The problem with this objection is that the term greater than in Greek and English can have one of two possible meanings. 

First, it could mean “someone who is better in essence as well as in position and rank.” For example, you would be greater than your pet, not just in your essence but also in your position and status. 

Secondly, the term ‘greater’ could also mean “someone who holds a greater status or office.” For example, your boss is greater than you; the president is greater than the vice president. However, the boss and the president are entirely human, and they have the same value, dignity, in the eyes of God. 

When Jesus said that the Father is greater, He did not mean it in terms of His essence but instead in His role and by virtue of status in heaven because when Christ uttered these words, He was on the earth and had assumed the position as a servant. 

Philippians 2:5-8 (NIV)

5. In your relationships with one another, have the same mindset as Christ Jesus:

6. Who, being in very nature God, did not consider equality with God something to be used to his own advantage;

7. rather, he made himself nothing by taking the very nature of a servant, being made in human likeness.

8. And being found in appearance as a man, he humbled himself by becoming obedient to death— even death on a cross!

Besides, we should also read the context of the Bible verses surrounding the passage in John 14 before we put in our assumptions. 

John 14:12-14 (NKJV)

12. “Most assuredly, I say to you, he who believes in Me, the works that I do he will do also; and greater works than these he will do, because I go to My Father.

13. And whatever you ask in My name, that I will do, that the Father may be glorified in the Son.

14. If you ask anything in My name, I will do it.

There are two critical things to take from this verse: first, Jesus said to ask in His name and not the Father’s name, showing He shared in the same authority. 

Secondly, the same Greek word for greater is used here; in this context, it cannot mean the “quality” of work; rather, it speaks of the quantity of works that Jesus did. The disciples collectively preached to more nations and people and did more miracles than Jesus, but they all performed the same kinds of works.