At its most basic, an indictment is basically when someone accuses someone of something in a formal and public manner. An example of an indictment: "Hey everyone! This guy stole a bunch of shit from that store. [Turning to the thief] I saw you do it and this other guy did too. We should all talk about how we know you did it (like what kind of proof we have) and what we should do to punish you for it."

In common parlance, it's the act of a state formally accusing someone of a crime (although procedurally, people are "charged" with crimes as a separate step).