It helps your muscles heal faster after workouts. I'll have one right after a workout and then early the next morning the day after the workout to help my muscles heal quicker. If I miss a protein shake, I'll notice a bit longer healing period the next day after I workout with weights. Not sure how to describe that, muscles just feel a bit more sore and for longer when I don't have protein after working out. I don't always use a protein shake for that though, I'll eat tuna or egg whites "fried" in coconut oil.
I use yellow pea protein powder and I've found it to be the best in terms of digestion. It never hurts my stomach like whey or soy protein powders. No protein powder I've ever tried makes me feel relaxed or energetic, it just feeds my muscles. I wouldn't advise consuming protein drinks only. It's not a complete source of nutrition unless you're using a meal replacement type. When I go without meat for awhile, I'll have more protein shakes than normal though. For example, one in the morning, then I'll have some fruit, one at lunch time, then I'll have a green salad, and one at dinner, then I'll have some sauteed veggies.