Bonjour is the Apple implementation of Zero configuration networking:
Among other things, it's used with iTunes for Home Sharing, syncing to Apple TVs and the Remote app. It's also used as a network printing mechanism from PCs (via Bonjour Print Services).
I'm sorry, but the Wikipedia anwser is too technical to help me. I compare that with someone whose answer to the question "What is DNA's function in life" replies with "ATCGGCTAATTGC...". What does Bonjour do? What accomplishes the same tasks in Bonjour's absence? What are the advantages of Bonjour over alternatives?" Thanks.