First things first, a First-Past-The-Post voting system is what we use currently. Basically, whoever gets the most percentage wins, even if a majority didn't vote for the said person. This anomaly in elections is called the spoiler effect, and prevents a candidate with a majority from winning if another candidate (ex. Ralph Nader in 2000) splits the vote .
An Alternative voting system (Or Instant Runoff Voting, IRV) is a solution that produces results almost identical to a First-Past-The-Post system, except for one thing, there is NO spoiler effect.
See more here: http://en.wikipedia.org/wiki/Alternative_voting