First, in the opening lines, Jonson establishes himself as one who is able to comment on his mentor: "To draw no envy, Shakespeare, on thy name,/Am I thus ample to thy book and fame;". Johnson himself was a proflic and popular writer. He is saying here that his works match that of Shakespeare's in both sheer page count and also in popularity.
However, Jonson quickly confesses that there can be no writer who has ever lived equal to Shakespeare's genius:
"The applause ! delight ! the wonder of our stage!
My Shakespeare rise ! I will not lodge thee by
Chaucer, or Spenser, or bid Beaumont lie
A little further, to make thee a room:"
Furthermore, his mentor has succeeded even these famous writers by equaling and surpassing even the most lauded writers ever: "Aeschylus,Euripides, and Sophocles" among them.
The theme of the poem truly can be understood in this single line: "He was not of an age, but for all time!"
Jonson, while he knows he is a good and respected writer, realizes that Shakespeare is in a class by himself and that his own talents pale by comparison.