What is meant by the expression that Jesus came in the fullness of time? What do they mean when they say "in the fullness of time Jesus came"? I want to know what the fullness of time means in this scriptural context.
Galatians 4:1-3 gives us a clue as to what verse 4 means.  I’m quoting from the New Living Translation Study Bible because it makes it very easy to understand:


  Think of it this way.  If a father dies and leaves an inheritance for his young children, those children are not much better off than slaves until they grow up, even though they actually own everything their father had. They have to obey their guardians until they reach whatever age their father set.  And that’s the way it was with us before Christ came.  We were like children; we were slaves to the basic spiritual principles of this world.


Turning now to verses 4 to 7 it explains that Jesus came at exactly the right moment in time, the time ordained by his heavenly Father, to free humanity from slavery (to the law) and to open up the way for believers to become sons of god, heirs to the promise.  Here are the relevant verses:


  But when the right time came, God sent his Son, born of a woman, subject to the law.  God sent him to buy freedom for us who were slaves to the law, so that he could adopt us as his very own children.  And because we are his children, God has sent the Spirit of his Son into our hearts, prompting us to call out “Abba, Father”.  Now you are no longer a slave but God’s own child. And since you are his child, God has made you his heir.


Why, then was this the right time?  I found an article that gives one Protestant view about the meaning of God sending his Son “in the fullness of time”.  It gives six reasons why the right time was 2,000 years ago.  The article also explains the significance of Daniel’s prophecy about the promised Messiah: 


  Christ came when He did in fulfillment of specific prophecy. Daniel 9:24-27 speaks of the “seventy weeks” or the seventy “sevens.” From the context, these “weeks” or “sevens” refer to groups of seven years, not seven days. We can examine history and line up the details of the first sixty-nine weeks (the seventieth week will take place at a future point). The countdown of the seventy weeks begins with “the going forth of the command to restore and build Jerusalem” (verse 25). This command was given by Artaxerxes Longimanus in 445 B.C. (see Nehemiah 2:5). After seven “sevens” plus 62 “sevens,” or 69 x 7 years, the prophecy states, “the Anointed One will be cut off and will have nothing. The people of the ruler who will come will destroy the city and the sanctuary” and that the “end will come like a flood” (meaning major destruction) (v. 26). Here we have an unmistakable reference to the Savior’s death on the cross. A century ago in his book The Coming Prince, Sir Robert Anderson gave detailed calculations of the sixty-nine weeks, using ‘prophetic years,’ allowing for leap years, errors in the calendar, the change from B.C. to A.D., etc., and figured that the sixty-nine weeks ended on the very day of Jesus’ triumphal entry into Jerusalem, five days before His death. Whether one uses this timetable or not, the point is that the timing of Christ’s incarnation ties in with this detailed prophecy recorded by Daniel over five hundred years beforehand.  Source: https://www.gotquestions.org/fullness-of-time.html


The article concludes that the timing of Christ’s incarnation was such that the people of that time were prepared for His coming.  World events had brought the Jews to a point in history where they were living in expectation of the promised Messiah.