Is it necessary to peel aubergine?
It depends.

The skin of aubergines can sometimes be a bit hard after preparation, especially if you are working with older fruit and apply dry heat (e.g. grilling). During cooking, the skin should get soft, but some people dislike the texture difference between the very soft inner flesh and the noticeable firmer skin. 

The decision to peel or not is similar to the question whether one should peel bell pepper or skin tomatoes - it depends on what one plans to cook and whether one objects to the texture. Leaving the peel on can help to hold slices together when grilling or frying slices. Or, one of my favorite preparations, the skin can be like a disposable container when grilling the whole fruit until the flesh becomes very soft, which can then be scooped out and puréed.

On the other hand, the color contrast between the dark skin and light interior can add visual appeal to a dish, some cooks remove only strips of the skin to create a pattern on the outside of aubergine slices.