In order to answer this question, you have to keep in mind some key details pertaining to each character. Dimmesdale, as you should know by now, is the father of Hester's baby. Chillingworth, is of course, Hester's long lost husband (Mr. Prynn). And most importantly, Hester is the only character who is fully aware of all of these things.
Chillingworth suspects Dimmesdale is Pearl's father from the very beginning. In order to bring this secret to light, he has attached himself to the minister as a doctor (or "leech"). He spends every day in close contact with this man, who is growing ever weaker as a result of his guilty conscious and outward hypocrisy. Chillingworth plays into both by making constant but casual reference to scientific and spiritual matters of secrecy.
This conversation in chapter 10, is one such reference. Dimmesdale, outside one day, questions Chillingworth about a strange looking plant. Chillingworth explains that the dark leaves of this plant growing on an unmarked tombstone are the sign of the buried's unconfessed sins. He is suggesting here, that even if a person goes to the grave, unconfessed sins will find a way to show themselves. Whether the story is true or not, Chillingworth here is making direct reference to his suspicion that Dimmesdale has an unconfessed sin. He is attempting to scare or warn the minister into confession.