The statement - A pure substance consisting of group of atoms with an unique atomic number, but with a varying mass number, which cannot be made into something chemically simpler is called an element.
This statement states that a element is made up of a group of atoms that have an unique atomic number (which is equivalent to the number to the number of protons and electrons). So, an element can be identified by its atomic number or its total number of proton and electrons, as it is unique. "varying mass number" - it refers to an element's isotopes.
To make it more clear-
Definition of ISOTOPE: any of two or more forms of a chemical element, having the same number of protons and electrons in the nucleus, or the same atomic number, but having different numbers of neutrons