Over the course of history, tea has been processed in different ways in the name of convenience for transport and consumption. Individual leaves have been rolled into pellets, and larger amounts of leaves have been molded into bird's nests. But perhaps no packaging method has impacted the way people consume tea as the tea bag.
For the manufacturer, the tea bag was an obvious benefit. It allows small bits of dust (fannings) to become a useful grade of tea. Tea could be marketed as a portable, mess free affair.
It is also useful for the tea drinker, if you want to take your tea on the go (making it easy to order a cup of hot water at a restaurant and still enjoy your favorites), if you don't have time to wash a tea infuser, or if you have a lot of people over, and you want an easy clean-up.