At first, Mr. Frankland of Lafter Hall comes across as a pretty minor character, one of Sir Henry's gentleman neighbors whom Doctor Mortimer mentions in passing when describing the neighborhood of Baskerville Hall. But he's more important to the plot than he seems.
Before we get to that, we'll just mention that, like Doctor Mortimer (skulls) and Stapleton (moths and butterflies), Mr. Frankland has an unusual hobby. For Mr. Frankland, it's lawsuits. As Watson puts it, Mr. Frankland "fights for the mere pleasure of fighting and is equally ready to take up either side of a question, so that it is no wonder that he has found it a costly amusement" (8.11).
Here's the first important thing we learn about Mr. Frankland: the mysterious "L.L." connected to Sir Charles Baskerville's death is his estranged daughter, Laura Lyons. Laura disobeyed her father by marrying a guy he didn't like, a penniless artist named Lyons who eventually deserted her anyway. Because of her disobedience, her father decides to disown Laura. Doctor Mortimer says that there may be "one or two other reasons as well" (10.61) for Laura's abandonment by her father, but the novel doesn't go into any further detail about what those other reasons might be.
What we do know is that Mr. Frankland gives her "a pittance" (10.63) to live on, but that most of the money that she uses to set up her typing business has come from Stapleton, Doctor Mortimer, and of course, Sir Charles Baskerville himself. Perhaps if Mr. Frankland had been a better father, she might not have gotten involved with Stapleton.
And here's Mr. Frankland's second contribution to the plot: since he's such a busybody, he uses his telescope to keep an eye on the moors when he learns that the convict Selden has escaped from the nearby prison. But when he does spot a man living out on the moors, a man who receives regular deliveries of food from a boy in Coombe Tracey, he refuses to tell anyone about it.
Instead, Mr. Frankland brags to Watson that "he could tell [the police] what they are dying to know; but nothing would induce me to help the rascals in any way" (11.82). Mr. Frankland resents the cops for being on the other side of one of his many lawsuits. And his general distrust of people keeps him from reporting someone he truly believes is an escaped psychotic killer.
Of course, the man who Mr. Frankland is watching on the moors isn't Selden the murderer. He's none other than Sherlock Holmes. Mr. Frankland accidentally gives Watson the clues he needs to find Holmes, but Watson has to trick Mr. Frankland into helping him.
Mr. Frankland is Doctor Mortimer's complete opposite: both of them reveal important plot details that give Watson new lines of investigation to follow. But Mr. Frankland does so unwillingly, because it's not in his nature to want to help. At least Watson is ready to manipulate Mr. Frankland a bit for a good cause. Bold move, Watson.