Mr. Micawber, as you will have noticed and as David more than once observes, is more than a little dramatic. In this section, Mr. Micawber has just finished conversing (with some effort) with David and has left him but has then been overcome by his "passion" for letter-writing and decided to commit his thoughts to a letter to David instead. As befits Mr. Micawber's character, he has decided to enliven his letter with a quotation from a well-known poem—in this case, Thomas Gray's famous "Elegy Written in a Country Churchyard." What he is saying, in closing with these lines, is that having done his duty and performed the act of "reparation"—which, if he had not done it, would have left him feeling unworthy to face his fellow humans—there is nothing left for him to do on earth. Indeed, the only thing left is for him to be "deposited" (buried) in the grave, where we all end up—it is a "place of universal resort."
The quotation from Gray simply describes how all our forefathers "sleep" metaphorically in their lonely cells, or coffins, beneath the ground. The word "cell" doesn't have the meaning of a prison cell, here, but rather refers to a monastic cell, a small room for contemplation.