The play ends with a crazy drunken party in celebration of the peace treaty that has just been signed between Athens and Sparta. At the party, the former enemies realize that the members of the opposing side really aren't so bad. Keeping things from getting too preachy, the Athenians suggest that, in the future, they should conduct all official diplomatic business while drunk—because it makes everyone get along, and smooths out misunderstandings. Wow. Who knew that the prototype of Drunk History was penned by Aristophanes?
The very final moments show Athenians and Spartans taking turns dancing and singing songs; this creates a spirit of equality and multiculturalism. Aw, shucks. This multicultural flavor gets symbolized again when last word in the play goes to the Spartan Delegate… this would have been interpreted by Athenian audiences as a big ol' olive branch.
These touches let the play end on a light, positive note, and show the humanity of both Athenians and Spartans—a major part of the play's message. You can bet that Aristophanes was hoping that this spirit of festivity and friendship would be infectious—and that his audience members would leave the theater inspired to make a peace treaty with Sparta a reality… after getting shmammered, of course.