A falsetto voice is a special way of speaking or singing where you speak in a higher pitched voice than normal. Imagine Mickey Mouse's talking style but with a fancy name. Actors do this sometimes, e.g. Robin Williams in the film Mrs Doubtfire or Kevin Clash when voicing the character Elmo in Sesame Street and Barry Gibb of the Bee Gees, with his R&B falsetto. Also, Kellin Quinn from the band sleeping With Sirens uses falsetto sometimes.
It is like stretching the mouth out into a wide smile and saying 'ee', except it is sung.