Artaxerxes I was the King of Persia during the time of Nehemiah and Ezra. During his reign, he halted the rebuilding of the Temple area that his predecessor Cyrus had allowed. Later, he allowed it to continue. During the seventh year of his reign, he allowed Ezra and a large number of Israelites to return to Jerusalem. Then in his twenty-first year he allowed Nehemiah to return to Jerusalem, and to rebuild the city walls.
Seventy Weeks Prophecy
Artaxerxes is associated with a prophecy found in the Book of Daniel. The angel Gabriel came to Daniel and told him that the Jews would have 70 7s to finish the transgression against God, to be done with sin, for reconciliation to be made, to bring in everlasting righteousness, to complete God’s revelation, and to consecrate the Holy of Holies. Then the angel said that after the decree to rebuild Jerusalem until the Anointed One would come there would be 7 7s and 62 7s. After the 62 7s the Anointed One would be cut off.  The "7s" are said to mean weeks of years, according to biblical scholars. After doing the math, there would be 49 years and 434 years, which adds up to 483 years.
There are multiple theories as to which decree was being referred to. Two of the possibilities were made by Artaxerxes.
Decree to Nehemiah
In 444 BC, in Artaxerxes' 21st year, he gave Nehemiah permission to go to Jerusalem to rebuild its walls. The Book of Nehemiah says that it was his 20th year when he gave Nehemiah permission. Nehemiah could have used a Jewish calendar that rendered the month of Tishri as the first month, which is in the fall. The decree was given in Nisan, in the spring. To Nehemiah, it was still Artaxerxes' 20th year. According to our form of reckoning time, it would have been the 21st year. If this is the decree referred to, 483 years from this point is about AD 40. This is much too late to be referring to Jesus. So proponents of this theory suggest that the 483 years are prophetic years, each of which contain 360 days. They then convert prophetic years to actual years using the following equation:
(x=prophetic year, y=actual year)
After applying this method to the Daniel prophecy, from the decree to the Crucifixion, there were 476 years and 3 weeks. Add 476 years to 444 BC and the sum is AD 33, which is one suggested year of when Jesus died.
However, this theory may be a bit of a stretch to assume that the prophecy used "prophetic years." Also, the prophecy said the Anointed One would come at the end of the 62 7s, and cut off after the 62 7s. This theory suggests Jesus was revealed as the Anointed One at the Triumphal Entry into Jerusalem, and then cut off afterwards. While this may indeed be the case, there is another theory that may better fit the evidence.
Decree to Ezra
In Artaxerxes' 7th year, in 458 BC, Ezra requested permission to go to Jerusalem. Artaxerxes granted Ezra everything he requested. This may have included rebuilding Jerusalem. The decree in Ezra 7 is broad enough to include the rebuilding of Jerusalem. Further evidence of this is that when Nehemiah heard 13 years later that the walls of Jerusalem were still destroyed, he was extremely saddened. He may have expected the walls to have been rebuilt by then, since they had the permission to do so. If so, then the 483 years could have began in Artaxerxes 7th year. The 483 years would then end at AD 26. This was when Jesus started his ministry, which can be described as the coming of the Anointed One. It would then be a few years afterwards when Jesus died.
We can know that Jesus began his ministry in AD 26 because in the following year, near Passover, Jesus cleared the Temple. The Jewish leaders said it had taken 46 years to build the Temple, after He suggested He could rebuild it in 3 days (referring to Himself as the Temple). Herod the Great began his renovations on the Temple in 20 BC, and 46 years from there is AD 27. Since this occurred in the beginning of the year, Jesus' ministry would have began in the previous year, AD 26.