The story of Cain and Abel is told in the first book of the Bible, Genesis. In Genesis 4, Adam and Eve, the first humans, after being expelled from the garden of Eden, bear two sons, an older son named Cain and a younger son named Abel. When God preferred Abel's offering to Cain's, Cain became jealous and murdered Abel. Then God cursed Cain, and he was cast out from his family. Eve had another child, Seth. According to this account, some people are descendants of Cain and some are descendants of Seth.
The first area in which this is relevant is that it suggests a human duality, with evil being inherent is some parts of human nature. Jekyll struggles to use medical technology to rid himself of the evil in his nature and, of course, fails.
The next point of relevance is that Mr. Utterson claims to "incline to Cain's heresy." This refers Genesis 4:9, at the point just after Cain has murdered Abel:
And the Lord said unto Cain, Where is Abel thy brother? And he said, I know not: Am I my brother's keeper?
Although Cain is lying here, the saying is emblematic of an attitude of selfishness and not bearing responsibility for others. Utterson is implying that there maybe a third route, a sort of neutral point between good and evil, where he stays out of the affairs of others. However, readers realize as the story progresses that this sort of neutrality is in fact a form of complicity, something that is signaled by the phrase originating with a person lying about a murder.