In John 14:12, Jesus said, "Truly, truly, 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 the Father."
His disciples were to carry on the work Jesus had begun. They could do so because He was going to the Father and would send the Holy Spirit.
By "greater works," did Jesus mean the so-called miracles we see performed by materialistic false teachers who promise God will intervene in a person's situation if they simply send money to this individual's "ministry"?
Did He mean the advancements we'd make in technology would enable us to perform "greater miracles"? Medical breakthroughs that prolong people's lives and even bring them back from the dead (i.e.: defibrillators). Advancements in food production and preservation that enable us to feed individuals who would otherwise go hungry. Machines that can dig wells in barren landscapes, providing abundant clean water for the inhabitants.
For the answer to what these greater works are, we must look to God's Word. First, we notice miracles typically occur in clusters. Second, the purpose of these miracles is to authenticate God's message. The miracles of Moses, Elijah and Elisha, Jesus and His disciples.
While God can and still does, on occasion, perform miracles through His followers, we no longer need Him to do so to make His message known. In verse 14, Jesus is not encouraging His disciples to become miracle-workers. In fact, He's doing the opposite. He is urging them to believe His words because they are His Father's words.
And these greater works? D. A. Carson says they are those done on the basis of Jesus's death, resurrection, and exaltation.  The greater works point to the power of the gospel transforming the lives of undeserving sinners. When Peter preached at Pentecost, 3,000 were born again. That's probably more than Jesus saw converted in His entire earthly ministry! We can see in Acts how the message kept spreading. It went all around Jerusalem and, eventually, to the Gentiles throughout the Roman Empire. J. C. Ryle said, when it comes to Jesus's statement that we'll do greater works than He did, "There is no greater work possible than the conversion of a soul."
Which would be greater? Being used as God's instrument to cure diseases, sicknesses, and raising the dead. Or . . . being used as God's instrument to save souls, so they don't spent eternity in hell?
How does sharing the gospel bring us comfort?
If you've ever helped someone because the Lord gave you opportunity to do so, you likely felt joy, peace, and hope. In other word you were comforted in your faith. How much greater would that joy, that peace, that hope, that comfort be if you shared the gospel with them and they came to saving faith!
Of course, this causes us to look to the God. When we see Him at work in our life or in the life of someone else, we become increasingly aware of His grace, love, and mercy. We begin to marvel at His awesomeness and we are comforted.
When we see the Lord at work, we are motivated to keep moving forward.
As we look at verses 13-14, I want to give a word of caution.
Jesus said, "Whatever you ask in my name, this I will do, that the Father may be glorified in the Son. If you ask me anything in my name, I will do it."
Jesus isn't promising that He will do any crazy thing we ask as long as we tack on the phrase "in Jesus's name." The context of "whatever you ask" is tied to doing Jesus's works. We are to pray in submission to God's will and ask Him to accomplish that will in and through us and others.
In context, this is referring to proclaiming the gospel. If we ask Jesus to help us present the Truth, He's going to do it. Now, how He helps us often doesn't line up with how we think He will or should. We are limited and cannot fully know the will of God. But He will help us declare the gospel. Further, we must remember that it is He who brings people to saving faith.
Isn't that comforting? It's like being hired for a job and you have no clue what to do or how to do it, and then your boss comes along and says, "Anytime you need help, just ask me. I'll help, no questions asked."
How would you feel? Less apprehensive? Hopeful? Maybe even encouraged? Comforted?
 The Gospel According to John [Eerdmans/Apollos], p. 496