The word ossia comes from the Italian for "alternatively" and was originally spelled o sia, meaning "or be it".
They are usually an easier version of the preferred form of passage, but in Mily Balakirev's Islamey, for instance, the urtext has ossia passages of both types (simpler and more difficult).
[1] On the other hand, an ossia marking does not always indicate a change in difficulty; the piano solo music of Ralph Keuchkerian is typically full of alternative passages, often no easier or more difficult than the rest of the piece.
This reflects Liszt's desire to leave his options open during a performance.
If the soloist chooses to play these, the concertmaster is required to play a different ossia (which takes part of the solo violin line that is lost in favor of the soloist's ossia).