In the various Cinderella stories we have read, the heroine is able to reach a better life using magic and marriage. In each case she is a "good" person: she is patient, kind, and intelligent; she does not disrespect those that treat her terribly, and she longs for a better life. In each case, a helper presents himself to aid the Cinderella character: a fairy godmother, birds, a cow, trees, etc. Each of these helpers uses magic to get the heroine into a good situation.
In real life, this magic cannot happen. The idea that a fairy godmother can turn a pumpkin into a coach is obviously not true. But are there other ways for one to go from rags to riches? I think so.
First of all, marriage is definitely possible as a means to improve quality of life. For an extreme example, look at a country like Haiti. Haitians know that if they can marry an American, they will be able to go live in America. This is not to say all Haitians are desperate to leave, nor that they all dream of marrying Americans; however this is a good example of how a marriage can really and truly take someone from one life into a completely different life. This exists within America too, surely, but we do not typically think Americans can be living as poorly as Cinderella originally lived.
I also think there are other examples of rags to riches that may not be perfect mirrors of Cinderella, but are similar. For example, many athletes can quickly go from being under-appreciated and overlooked to celebrated and famous (see: Jose Bautista, Jeremy Lin, Brady Anderson, Tom Brady, Jacoby Ellsbury, the Miracle on Ice team, etc.).
In Michael Lewis' Moneyball, two players in particular are presented as completely unwanted: Scott Hatteberg and Chad Bradford. Hatteberg, apparently too injured to play, thought his baseball career was over; Bradford, who pitched in a most unconventional style, was never considered a real pitcher. Billy Beane, however, saw through the "outer ugliness" of both players - an ugliness that is comparable to Cinderella's dirty clothes and lack of social position - and signed them to play for his team, where they became, like Cinderella, stars. In order for this comparison to work, Beane would have to be considered both the helper and the Prince.
Cinderella and stories like hers are important because they give people hope. They help people believe that if they keep working hard, pushing through, enduring and persevering, that one day they could be rewarded.