What does it mean?
A “worthy one” or “pure one”; a person whose mind is free of defilement (see kilesa), who has abandoned all ten of the fetters that bind the mind to the cycle of rebirth (see saṃyojana), whose heart is free of mental effluents (see āsava), and who is thus not destined for further rebirth. A title for the Buddha and the highest level of his noble disciples.
-from Access to Insight
Why does it matter?
Here is a work that can cause an argument in the right setting! For Theravadans Arahats are fully enlightened beings with enlightenment every bit as complete as the Buddha himself. Indeed, in the suttas the Buddha called himself an arahat.
For a Mahayanist, Arahats are selfish bastards who only care about their own enlightenment, not the enlightenment of all beings.
I have a guess about why this happened. It’s only a guess, but here it is: once Buddhism became the state religion, huge amounts of money started to flow into its coffers. It went from being a practice for poor renunciates to the province of at least some powerful Abbots and University Administrators. Corruption was inevitable, and eventually a reformation was needed. Unfortunately, that reformation ended with some corruptions of the original teachings. A similar process happened with Christianity.
Of course, all this is assuming that arahats are real to begin with. For someone outside of Buddhism, the idea is pretty strange. An ordinary person living in this world having a spiritual experience so powerful that they come to an end of suffering? And of course, even mentioning rebirth can start a fight in some quarters. “Hindu backsliding!” “What is reborn!” Sigh.
I think in the end it’s impossible to know for sure if enlightenment is possible. It something that requires faith. Oh, you thought Buddhism didn’t require faith?