This new tense is not just used for past actions but every time we want to stress the fact that the action is a simple, straightforward, definite, once-and-for-all one:
for simple, specific aspect.
past time: He came, saw and conquered.
infinitive: I want to leave (now, once and for all, not keep on leaving)
imperative: Shut up! (once and for good)
participle: Coming to the door he said... ἐλθών
meaning: he came to the door and said... or
meaning: having come to the door ... (simple aspect)
NOT: while coming ἰὼν (ἐρχόμενος) (progressive aspect)
Examples from the text:
2nd aorist, active voice:
ἡ δὲ Μυρρίνη ἐπεὶ ἔμαθεν when she learnt [once]
2nd aorist middle voice
τί ποτε ἔπαθεν ὁ παῖς; Whatever [specific thing] happened to the boy?
εἰσήγαγεν αὐτούς he lead them in [once, NOT repeatedly]
πάντα εἶπον they told all [once]
ὁ δὲ Φίλιππος δεινὰ ἔπαθεν suffered terribly [one specific terrible ordeal]
ἐπεὶ ἀφίκοντο when they arrived = once they got there
2nd aorist participle
τί ἐγένετο; What [on earth] happened?
ὁ δὲ ἀδελφὸς πρὸς τὴν θύραν ἐλθὼν καὶ ἰδών...
2nd aorist imperative
having come and seen = he got to the door, then saw them and then....
εἰς τὸν ἀνδρῶνα εἰσελθόντες having once gone into the men's quarters
εἴπετέ μοι tell me [once and for, not: keep on telling]
εἰσέλθετε καὶ εἴπετέ μοι τί ἔπαθεν ὁ παῖς
ἐλθὲ δεῦρο come here [now, not again and again]
NOT in the text, but in the grammar section:
2nd aorist: infinitive
You must tell me [once and for all]: δεὶ ὑμᾶς εἰπεῖν
You must come in [at once]: δεὶ ὑμᾶς εἰσελθεῖν
You must see this! [once and for all]: δεὶ ὑμᾶς ἰδεῖν τοῦτο