Theland, we've talked about this before, but never mind. Buddhists believe that compassion and love bring happiness and well-being. Nirvana is a state free of desire, selfishness, suffering, or further rebirth, in which a person simply is, and is completely at one with his surroundings. If Nirvana, were, as you say, 'ceasing to exist', common sense tells you that human beings wouldn't aim to achieve it.
This is a simply overview of Buddhism, and quite honestly, I can't find fault with it. Can you?
http://www.buddhanet.net/e-learning/5minbud.ht m