In this essay, "Oxford in the Vacation," a part of Charles Lamb's collection entitled, Essays of Elia, the author (writing under the pseudonym "Elia") speaks of pretending to be what his is not.

In the essay, Lamb notes that he spent many of his younger years at "Christ's," short for Christ's Hospital, a "traditional English boarding school." It was "bleak and full of violence." Because of the connections of his family through his father's employer and—it is suggested—perhaps because of Lamb's amiable disposition, he escaped most of the aggressive behavior of the brutal headmaster, Rev. Mr. James Boyer. Lamb was also able to return home regularly to friends and family, which also made his life immeasurably easier. (It was here he met his lifelong friend, Samuel Taylor Coleridge.) Lamb's recollections in this essay of his time at Christ's refer to the training he received with regard to the church.

I was as good as an almanac in those days. I could have told you such a saint's day falls out next week, or the week after.

With this background at Christ's, Lamb was able to visit Oxford as an adult, and walk the halls and grounds—perceived by others to be a man of "degree or standing," which he was not. He had to leave school early, due to a stutter...

...this "an inconquerable impediment" in his speech deprived him of Grecian status at Christ's Hospital and thus disqualifying him for a clerical career.

While his classmates (including Coleridge) went on to Cambridge, Lamb's education ended at fourteen, when he had to go out to work. When Lamb speaks of fitting in at Oxford, it is as if he can pretend to experience what he missed because of leaving boarding school so early and never having had the chance to attend school at the university level—he uses the word "defrauded." He also notes that there was "nowhere...so pleasant" as Oxford, for one like him.

Your quote refers to Lamb's vacation (which was also vacation time at Oxford), when he enjoyed "idle weeks" soaking in a world he had missed when unable to attend Cambridge.

Then, to take a peep in by the way at the butteries, and sculleries, redolent of antique hospitality...ovens whose first pies were baked four centuries ago; and spits which have cooked for Chaucer! 

Those who work there curtsy to him out of respect. He wears black, something that also adds to the illusion that he belongs there. For Lamb, this vacation is a chance for him to see the academic world that was taken from him when he was forced to leave Christ's. In some sense, he is able to make right as an adult, that which he was prohibited from experiencing earlier. And this fills him with a sense of deep satisfaction—for he appreciates the antiquity there. His imagination runs rampant in perceiving life in those buildings many, many years before. Spending time in such a place would never have been wasted on Lamb: it would have been a humbling, yet gratifying, experience.

The quote in question is placed in the middle of the recollection of his visit to Oxford, and refers to that which he missed as a young man after leaving boarding school.