In ancient Athens, two types of suit could be
brought before the court: a civil dispute over some perceived private wrong
and a public indictment over a perceived wrong against the state. In either
case, a private citizen (or groups of citizens) needed to initiate the process.
Socrates, of course, is faced with a public
indictment, while Euthyphro, as you will see,
is initiating a private suit against his father.