Given the background of the Apology by Plato what do you think Socrates means by this and how is it relevant to the Athenians or to us for that matter?
At the end of the Meno, Socrates says that if Meno can convince Anytus of the things they have concluded in the dialogue he will provide a benefit to the Athenians.
This is a great question. As you know the Apology is the work that defends Socrates's actions and decision to take the punishment of the Athenians government, even though it is unjust. More particularly, Socrates is trying to convince his inner coterie of followers that death is not such a bad thing. After all, he will be released from his physical body and be able to engage in what really matters - philosophy. He will be able to contemplate the eternal forms. He also tries to convince his followers that they should obey the laws of the land, even if at times it is unjust (like in his case).
In light of these two points, the benefit that is in view is the emphasis on philosophy. If Socrates is able to convince his followers that there is nothing more important than philosophy, that is, the ability to see reality for what it is, then he has done his job. If his followers, in turn, will be a "gadfly," the term he used for himself, towards the city of Athens, then his followers would be doing their job. All of this would be a benefit in that there would be more philosophers.