Fractions represent parts of a whole and have two parts - a numerator and denominator. The numerator is the number on top and represents the parts, while the denominator is on the bottom and represents the total parts of the whole. There are three types of fractions: proper fractions where the numerator is less than the denominator, improper fractions where the numerator is greater than the denominator, and mixed fractions which are an improper fraction combined with a whole number.