The chapter gives some background info on Mr. Lydgate. Even though no one in Middlemarch believes that he's really a better doctor than Dr. Sprague and Dr. Minchin, the two physicians, they can see that there's something uncommon about him.
He was orphaned when he was just out of high school, and had been studying medicine practically since he could read.
He's a surgeon, rather than a physician.
(Being a surgeon didn't require an advanced degree, which is why he's "Mr. Lydgate" instead of "Dr. Lydgate.")
Surgeons weren't looked up to as much as physicians, so Lydgate has to fight through his own lack of social standing, as well as traditional notions about medicine, if he wants to change anything about the medical practice in Middlemarch.
We also learn that Lydgate fell in love with an actress while he was studying medicine in Paris.
He went night after night to go see her play, in which she murders her husband (who was played by her actual husband).
One night, she "accidentally" stabbed him for real, and Lydgate went to comfort her.
Turns out, though, that she had done it on purpose, because he was starting to bore her.
Lydgate was totally depressed by the news, and resolved never to fall in love again.