A set is a well-defined collection of objects where the objects are called elements of the set. A bag is an example of a set, as it contains well-defined objects like pencils, erasers, and books. For a group to be considered a set, the elements must be well-defined - for example, a group of boys would be a set because the number of boys is well-defined, whereas a group of beautiful girls would not be a set because beauty is not well-defined. Sets are represented using capital letters and curly braces, with individual elements represented by lowercase letters, and elements cannot be repeated within a set.