A trivial example may help to illustrate the distinction. It is an essential property of bachelors that they are unmarried, but it is an accidental property of bachelors that they have brown hair. This is because it is logically impossible to find a married bachelor anywhere in this or any other possible world, and therefore the property of being unmarried is an necessary or essential part of being a bachelor. On the other hand, brown hair is a contingent or accidental property of bachelors since some bachelors have brown hair and others do not. Even if for some reason all the unmarried men with non-brown hair were killed, and every single existent bachelor had brown hair, the property of having brown hair would still be accidental, since it is the case that in some possible world, a bachelor could have hair of another color.
There are various categories of accidental properties in Aristotle's logic, including number, quality, place, time, relation to other objects, etc.