What is a wasted vote?
Under FPTP, a wasted vote is a vote cast for a party in the near certain knowledge/belief that the party cannot or will not win that election.
The vote is 'wasted' as regards that electoral outcome because despite being cast it is known, before the event, that it will not make any difference to the result.
People may vote in this way for any number of reasons - primarily it is probably to show their support for a party/cause in the hope/belief that it will encourage other to offer more support in future and so a vote for the party will then no longer be 'wasted'.
Does AV remove the necessity for these people to 'waste' their votes in this way? Yes, it does.
Under AV, you can give a preference (vote) for a party who you are pretty certain will not win (to show support, encourage other in future etc), but you can also give preferences to other parties who are considered to have a chance of winning the election.
So a voter can use a high preference to show support and encourage others in future, but also ensure that their vote will be transferred to a more likely candidate if their top preference is knocked out.