While the Lord Jesus walked the earth during His three-year ministry, He taught His disciples and those who followed Him in Parables. Many times, He interpreted (explained) them, but the one about the fig tree was not explained.

Luke 13:6-9 King James Version (KJV)

He spake also this parable; A certain man had a fig tree planted in his vineyard; and he came and sought fruit thereon, and found none. Then said he unto the dresser of his vineyard, Behold, these three years I come seeking fruit on this fig tree, and find none: cut it down; why cumbereth it the ground? And he answering said unto him, Lord, let it alone this year also, till I shall dig about it, and dung it: And if it bear fruit, well: and if not, then after that thou shalt cut it down.

Christ in explaining to the Jews the coming kingdom of heaven on earth warned them of what was happening. Christ came to present himself as their Messiah one who was to be the ruler of Israel (all earth). As promised in Isaiah 9:6 King James Version (KJV) For unto us a child is born, unto us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counsellor, The mighty God, The everlasting Father, The Prince of Peace.

As well as in many other Old Testament Scriptures. What was about to happen to Israel was being fulfilled right before their eyes.  There are four key words in the parable: fig tree, fruit, three years, and this year.

The Fig tree was Israel.
The fruit was supposed to be their acceptance of him as their Messiah.
The three years were his ministry on earth where he presented them the opportunity to accept him as their Messiah.
The request for this year was for one more year (after His resurrection).

He again warned them of the coming kingdom in Luke 21:29-31. And he spake to them a parable; Behold the fig tree, and all the trees;When they now shoot forth, ye see and know of your own selves that summer is now nigh at hand.So likewise ye, when ye see these things come to pass, know ye that the kingdom of God is nigh at hand.

This year was fulfilled during the first 8 chapters of Acts where Israel, through the Apostles preaching and teaching was presented many more opportunities to accept the risen Christ as their Messiah. When the stoning of Stephen took place (Acts 7) the year was up and the fig tree was cut down.

God closed the door to the Nation of Israel and selected Saul (Paul) to go to the Gentiles with the message of salvation through faith (Acts 9 see vs 15-16). The door of salvation was opened to the Gentiles. The Jews were set aside, blinded (Romans 11:7-11,25). But one day, until the fullness of the Gentiles be come in, and the blindness will be lifted and God will again be dealing with His people, Israel.