The quote means that Atticus is a great man who stands behind what he says and does, behaving the same in public as he does in his home. Unlike him, the others are two-faced, for example, publicly attacking Tom Robinson, while believing in the comfort of their homes that he might be innocent.
Dr. Lanyon has learned damaging new information about Dr. Jekyll. I know this because after Utterson asks if Lanyon has seen Dr Jekyll, his face changes and he says he never wants to see him again.
He says this to reassure ralph that things will be ok. Simon is one of the most sensitive characters in the book and becomes aware of Ralph's worry. This is also an example of the books theme of herd mentality and social reliance since simon is aware of the effect his words and examples have on the others.