Before I explain why loose tea is better, I just want to let you know that I am mainly talking about generic supermarket tea bags. There are some excellent bagged teas out there, made up of whole tea leaves. Quality tea merchants often carry bags as well as loose.
The main difference between loose teas and bagged teas is the size of the leaves. That's what effects the resulting cup of tea. Tea leaves contain chemicals and essential oils, which are the basis for the delightful flavor of tea. When the tea leaves are broken up, those oils can evaporate, leaving a dull and tasteless tea. Typical tea bags are filled with the tiniest pieces of broken leaves, called fannings. Loose teas are typically whole leaves or at least large pieces of leaves.
On top of the leaf size, there is also the space factor. Tea leaves need space to swell, expand and unfurl. Good water circulation around the leaves is important, which doesn't typically happen in a cramped little tea bag.
A quick aside: the declaration of "Orange Pekoe" that you'll find on boxes of tea bags doesn't refer to the flavor or kind of tea. Orange Pekoe is actually a grade of tea. It's a good grade, but not a great grade. The grade is based on leaf size, but even Orange Pekoe tea is an inferior tea to a true whole leaf tea.
Even if you prefer a simple cup of black Keemun, or Assam (which is the major component of most bagged teas), try getting your tea loose instead of in bags. If you enjoy a change now and again, you can get a wide variety of teas in bags, but there are many more to choose from if you shop for loose tea.