Sometimes nutrients are added to starters and to all-extract brews, or to brews with a high level of adjuncts like corn, rice, or sugar. In general, yeast nutrient is not needed for most AG and PM beers.
We use only bottle spring water for our beers and we were getting kind of bad yeast attenuation. Finally it occurred to me that the purified spring water doesn't really have all the minerals of tap water.
I picked up some yeast nutrient and I have added it in the last several beers. Suddenly my attenuation is up 10% or more than it was previously. I don't have any scientific proof that it is the nutrient but it's the only thing I've changed from the previous 50 or so batches. I do know that my beers have gotten better and I'm hitting the FG easier and more often.
I started using Wyeast nutrient because it is a small price to pay for a little insurance--it only takes 1/4 teaspoon for a 5-gallon batch. I liken it to taking a multivitamin supplement every once in a while even though you know you eat a balanced diet.