Aristophanes was the most famous comic poet of ancient Greece and author of The Clouds, a play about Socrates that is actually mentioned in Plato's Apology as having been brought forward as evidence against Socrates at the trial of Plato. Because Aristophanes is a comic poet, Plato makes him give a very funny speech in Symposium. He accounts in the speech for the origin of love as being due to people originally having been welded together as beings with two parts; thus for every person there is a missing half necessary to restore the person to completion as a full human. Love is the search for that completion. The sense of the Greek text, as Aristophanes' plays, includes many double entendres and slapstick and sexual humor.
While Aristophanes tells Eryximachus twice that his speech is not intended as a joke, it is not hard to tell that it comes from the imagination of a comic playwright, particularly if we understand "comic" as meaning far more than just "funny." Rather than present a speech of carefully crafted rhetoric, Aristophanes gives us a myth that is wildly imaginative and very entertaining. The story is pleasant enough and has an uplifting conclusion, with the suggestion that Love helps us to find our "other half" and that one day we might be fully reunited.