This is what I am gathering from this example. As you said you are dealing with the two imperfective verbs meaning 'to carry.' The difference:

Носить - to carry (multi-directional, or multiple times)
Нести - to carry (unidirectional, one time)

The last example: "Я несу тебе кофе." - Means "I am brining you coffee." It is is implying she is going directly to him, and the action is occuring one time at the moment.
The other examples with prefixed "при" can be interpreted as multiple times. "Она приносит ему полотенца." She brings him towels, which could be interpretted as many times.

That is my understanding of it. It also doesn't hurt to know which verbs of motion belong to "group 1" or "group 2", because when prefixation occurs, generally, group 2 verbs remain imperfective, and group 1 verbs become perfective.

Приносить - to carry (Imperfective)
Принести - to carry (perfective)