The social conflict in Dr. Jekyll and Mr. Hyde is the double-dealing struggle between good and evil. Stevenson's society was greatly concerned with the duality in humankind's inner nature. It was a duality that led to good, like Jekyll's "futherance of knowledge or the relief of sorrow and suffering," and to Hyde's evil that was "inherently malign and villainous." Jekyll himself sums it up when he writes that the "polar twins" of good and evil were "continuously struggling."
The moral conflict is the battle Jekyll wages within himself about the rightness and wisdom of yielding to Hyde. This is particularly pronounced in the end of the story but exists at the beginning as well since Jekyll is absolutely positive to keep his experiments and dark life a deep secret. In addition his experiments themselves presented a subtext of moral conflict because of the danger inherent within them, carried out as they were upon his own person:
I knew well that I risked death; for any drug that so potently controlled and shook the very fortress of identity, ... [might] utterly blot out that immaterial tabernacle which I looked to it to change.
The physical conflict is the great physical change that overcomes Jekyll coupled with the physical atrocities that Hyde does not hesitate to commit. Our first introduction to Hyde is through the story Enfield tells Utterson about his ghastly midnight encounter with Hyde, the gruesome stranger
I had ... a loathing to [the] gentleman[Hyde] at first sight. ... But the doctor's case was what struck me. ... every time he looked at my prisoner[Hyde], I saw that Sawbones turn sick and white ....
who has keys to and entrance at Jekyll's shabby, neglected laboratory door: "he carried us but to that place with the door? -- whipped out a key, went in, ...." The quote above underscores a third physical conflict, that of the overwhelming revulsion and violent hostility people feel in the presence of Hyde.