What does "To-may-to, to-mah-to" mean?

It refers to the George Gershwin song, "Let's Call The Whole Thing Off", which is a duet between two characters from different social classes, and therefore different accents.

You say eether and I say eyether,

You say neether and I say nyther,

Eether, eyether, neether, nyther,

Let's call the whole thing off!

You like potayto and I like potahto,

You like tomayto and I like tomahto,

Potayto, potahto, tomayto, tomahto!

Let's call the whole thing off!

Nowadays, it's often used when someone feels that the same thing is being referred to using different words.

"I think David Beckham is past his best"

"Well, he's not as young as he was"

"Oh, tomayto, tomahto"

It refers to different ways of saying tomato. It means it doesn't matter whether you say it with a different accent, it's still the same thing. So the expression means: it doesn't matter.

It's a way of dismissing a noted or claimed or supposed difference between two things as trivial.

Attitudinally, it combines an acknowledgement of some difference while simultaneously waving that difference away as not worth bothering with.

And because the pronunciation "to-mah-to" is, at least to ears attuned to US pronunciation, connotatively "upper class," the dismissal gains a subtle heft since to insist on the validity of the "obviously" a trivial difference makes one fussy and highfalutin, a stickler and a snob over petty differences. And that's always a no-no.

There's a class game neatly embedded into the expression, which is there even without benefit of the lyrics from which the phrase was spun-out -- testimony to the verbal genius of Ira Gershwin (though I might have guessed it was Cole Porter, who was also capable of such a feat.)

@Theta Thanks for that great link!