The 3 roles were intended to be played by 1 actress. The 3 women (that we see in the movie) that have a significant role in Joe's life are all, really, the same woman.
I think it's a comment that the relationships we have in life, successful, unsuccessful, and even recognized but not pursued, all have a common element that sets those people apart from other people in our lives. And, while there's an often crooked path to get to the right one, it's that element that keeps us trying to find them. Last, just as Joe doesn't recognize the resemblance between the 3 characters, we don't always notice the common elements in our relationships, or notice them for what they are (so we sometimes are drawn to people who have that element, but who are otherwise not right for us at all).
That's what the 3 Meg Ryan roles said to me. And it sort of comes close to summing up the whole movie for me... we sometimes have to follow a twisted/crooked path in order to find self actualization ... and we come across the same elements and challenges (Meg Ryan, the path, etc.) in our life over and over again until we get those things taken are of.
I think Meg Ryan plays all three roles because she is what Tom Joe has been looking for in women all his life. He even tells her that at the end when they're about to jump into the volcano. Maybe the other women just looked like Ryan's final incarnation, because that's what Joe wanted them to be.