the breaking of a command that was already given: stepping across a line someone had clearly drawn
The picture inside this word is a physical one. A boundary has been marked, and someone walks over it. That image is what separates the word from the general vocabulary of wrongdoing: it does not merely say that a person did wrong, it says that a rule was already in force, that the line was in plain sight, and that the person stepped past it anyway.
Because the line has to be there first, the word only works where a command has actually been given. Paul builds an argument on exactly that point when he says that where there is no law, there is no transgression (Romans 4:15). He can still insist that sin was in the world long before Moses, because the broad word for sin (ἁμαρτία) does not depend on a published rule. This narrower word does. Adam is the obvious case, since he had one direct command to break (Romans 5:14), and so is Eve, who is described as the one who crossed the line (1 Timothy 2:14).
In the plural the word gathers up a whole record of such crossings. The law was added on account of them (Galatians 3:19), and what Christ's death buys freedom from is the accumulated violations committed under the first covenant (Hebrews 9:15). Hebrews also sets it beside a companion word for refusing to listen (παρακοή), the pair covering both the command crossed and the voice ignored, and says that every one of them drew the penalty attached to it (Hebrews 2:2).
So the word carries a sharp edge of accountability. Where the word for a false step (παράπτωμα) pictures a wrong as a stumble off the path, this word pictures it as a step across a boundary the person could see.