In Catholic teaching an omission is a failure to do something one can and ought to do. If this happens advertently and freely, it is considered a sin.
The degree of guilt incurred by an omission is measured like that attaching to sins of commission, by the dignity of the virtue and the magnitude of the precept to which the omission is opposed as well as the amount of deliberation.
A person may be guilty of a sin of omission by failing to do something which he is able to do and which he ought to do, by reason of a cause for which he is entirely responsible, as when a person knows that drinking to drunkness will incapacitate him, and yet drinks.
Paul the Apostle refers to this sin directly when he states "For I do not do the good I want ..." (Romans 7:19).
James the Just more exactly defines this sin when he states, "Whoever knows the right thing to do and fails to do it, for him it is sin." (James 4:17)
Another way to phrase the sin of omission would be to say "He who has the ability to act on an injustice, but who stands idly by, is just as guilty as he who holds the knife." ~~Dracano Sapien
"In the end we will not remember the words of our enemies, but the silence of our friends" ~~Martin Luther King
This article incorporates text from a publication now in the public domain: Herbermann, Charles, ed (1913). Catholic Encyclopedia. Robert Appleton Company.