When someone respected and well known dies we consider their final words to be important and significant, a distillation of that person's wisdom throughout their life. The most important last words spoken were spoken by Jesus to disciples who were to be his witnesses, taking the gospel to the whole world.
Jesus' teaching and example investigated here are not strictly 'his last words'* but his meeting in the 'upper room' was the last time he saw his disciples together before being arrested and put to death.
If these were just the words of a man they would be significant; the wonder is that Jesus knew exactly what was going to happen and so carefully prepared his church for what was going to come. We are seperated by two thousand years from this event, yet there is a real sense in which we are also in that room, able to learn from his last words.