An epitaph is a tribute written to someone dead. The epitaph of "Elegy Written in a Country Churchyard" is often taken to refer to Gray himself and what he thinks might be written about him after he dies. It states:
Here rests his head upon the lap of Earth
A youth to Fortune and to Fame unknown.
Fair Science frown'd not on his humble birth,
And Melancholy mark'd him for her own.
But the verse is also sometimes interpreted to simply be the epitaph to an anonymous poet. Therefore it is a riddle.
However, if it refers to Gray, it is significant because it shows that he identifies with all the humble, unknown souls lying in the country churchyard. He is not setting himself above them, but states he is equally obscure. Like them, he has not been born to fortune, which would be high rank or money.
However, given that he is praising these simple people for their worthy if unsung lives, he would appear to be equally praising himself in his epitaph. If he is praising himself for his obscurity, it is ironic, because he has become a famous poet, still read centuries after his death.