Since mayonnaise is made with eggs it technically has animal fat in it. Those who consider themselves to be vegan will want to avoid eating mayonnaise because of the fact that it contains an animal by-product in the form of eggs. Regular mayonnaise tends to be high in saturated fat, though there are certainly low-fat and non-fat alternatives for those who are on a diet.
While there may be some benefits to eating animal fat because of certain nutrients that can be found in it, generally it is not a good idea to eat too much of it on a regular basis. Mayonnaise itself though contains a few different vitamins which are important for a healthy well-rounded diet.