An unknown visitor has come by the house that Sherlock Holmes and John Watson share, but they weren't home to meet him.
Watson inspects a walking stick that the visitor mistakenly left behind.
Watson notices that it's made of nice wood and it has a band of silver under the handle dedicated "To James Mortimer, M.R.C.S., from his friends of the C.C.H.," dated 1884 (1.1).
Watson guesses that the stick belongs to an older country doctor, and that it was a present from the local hunting organization.
(Watson is talking about fox hunting, the classic British sport of the upper classes that involves hunting down foxes on horseback with a bunch of dogs—total Downton Abbey stuff.)
Holmes breaks the news to Watson: he's mostly wrong.
But his dumb ideas have helped Holmes to get the right idea.
(We're only slightly exaggerating how tactless Holmes is with Watson.)
Yeah, James Mortimer is a doctor ("M.R.C.S." = "Member of the Royal College of Surgeons"), and he does live in the countryside.
But the "H" in "C.C.H." probably means hospital rather than hunt.
Holmes concludes that Mortimer must be a young man who did his medical residency at the Charing Cross Hospital before moving out to the countryside to start his own practice.
Also, Holmes guesses from tooth marks on the stick that Dr. Mortimer owns a smallish dog.
According to Holmes's records, there is a Dr. James Mortimer living in Dartmoor, in a town called Grimpen.
Just then, Dr. Mortimer appears at their door, and it's all as Holmes says.
He's young, he has a smallish dog, he left Charing Cross Hospital some time ago to set up his practice in the countryside (because he got married and settled down—that part, Holmes missed).
Dr. Mortimer is here because he has a most extraordinary problem (dun-da-DUN-dun).