How does tea flavor spread from a tea bag through a cup of hot water?

The tea in the bag is dehydrated, or dried out. Usually, it is also broken up or shredded inside the fiber bag. The bag is very porous, allowing hot water to rehydrate the tea leaves in the bag. as the leaves soak up the water, the natural juices trapped in the dehydrated tea leaves escape into the surrounding water, it's called dissipation.

If you pull the tea bag from the hot liquid, and squeeze it, the more concentrated juices trapped within the bag can be seen scattering into the surrounding clear liquid. This process also forces loose some of the oils trapped in the leaves, which tend to be bitter in flavor.

The process by which we allow the tea bag to sit and swell, releasing it's juices into the hot water undisturbed, is called steeping. A properly steeped cup of tea, will allow a minimum amount of the trapped flavor to blend with the water, and not become bitter.

For this reason, Tea is often brewed without heat, as in Sun tea for Iced tea. The tea bags are allowed to steep undisturbed for several hours in cold water, with only the rays of the sun providing heat to gradually coax the juices from the tea leaves, without releasing the more bitter oils.