In the essay, "Self Reliance," what does every person realize at some moment in his education?

Emerson states specifically that every man comes to realize that envy is ignorance and imitation is suicide. The passage in question reads as follows:

There is a time in every man's education when he arrives at the conviction that envy is ignorance; that imitation is suicide; that he must take himself for better for worse as his portion; that though the wide universe is full of good, no kernel of nourishing corn can come to him but through his toil bestowed on that plot of ground which is given to him to till. 

When Emerson speaks of the plot of ground that is given to him to till, he is speaking metaphorically. What he means is that each person has certain interests, tastes, and talents that make him unique. He cannot be content with his life, and he probably will not be successful in life, unless he finds out who he is, what he can do that fits his character and personality, and how he can best survive in the ongoing struggle for existence. 

The world's literature is full of similar advice. Shakespeare has Polonius tell his son Laertes in Hamlet:

This above all, to thine own self be true...

The Bhagavad-Gita, which Emerson knew, says:

You must learn what kind of work to do, what kind of work to avoid, and how to reach a state of calm detachment from your work.  

The best time to find out who you are and what you should do in life is when you are in school. It is easy to get started on the wrong foot when you are young. Choosing a major in high school and college can start you on a road in life which you may find is not right for you. Then it is hard to turn back and start all over again. Most schools have counselors and various other services to help students choose the right career goals for themselves. It is well worth the time and effort to take vocational aptitude tests and any help that will guide a student in the right direction. We shouldn't just imitate someone we admire, or envy. That person can turn out to be entirely different from us as we grow older and can disappear. That is what Emerson means when he says "imitation is suicide." 

Emerson may be mistaken in saying, in effect, that "every man" arrives at the conviction that he has to find, metaphorically, the right plot of ground to till. Unfortunately, there are many people who end up tilling the wrong plot of ground all their lives--or until it is too late for them to turn back. Robert Frost seems to be toying with this common phenomenon in his famous poem "The Road Not Taken."

I shall be telling this with a sigh
Somewhere ages and ages hence:
Two roads diverged in a wood, and I—
I took the one less traveled by,
And that has made all the difference.