(I made a mistake above and bolded the change)
Imagine three choices for candidates, X, Y, and Z. They're ranked 1, 2 and 3 by the 100 voters.
X gets 40 first choice votes, Y gets 35 first choice votes, and Z gets 25 votes.
Under the current system X wins. However, under AV, Z is eliminated, but for the people who put Z as their first choice, their second choice votes are shared out.
Imagine of the 25 people who voted for Z, 20 put Y as their second choice, and 5 put X as their second choice. They are added to the original votes.
X now has 45 votes. Y has 35+20 votes = 55 votes. Therefore Y wins.
However, if those 25 votes were split evenly (or 12 + 13), X still wins. It doesn't change things massively
It's almostly like X factor (except rather than voting on a week by week basis, it's done instantly), and it's simple.