So if #Z=1#, the element is #"hydrogen"#,
And if #Z=2#, the element is #"helium"#,
And if #Z=3#, the element is #"lithium"#,
...........................
And if #Z=24#, the element is #"chromium"#.
#Z# thus defines the identity of the element. You won't have to remember these numbers, because you should be given a copy of the Periodic Table in every examination in Chemistry and Physics you ever sit.
And the next concept to grasp is that of #"isotopes"#, for which we will take hydrogen as an exemplar.
If #Z=1#, then the element is hydrogen by definition; i.e. its nucleus contains the ONE positively charged nuclear proton. But the nucleus can also contain various numbers of neutrons, massive nuclear particles of zero electric charge. Most hydrogen nuclei contain NO neutrons, and we identify this isotope as #""^1H#, the #"protium isotope"#. A few hydrogen nuclei contain 1 neutron to give the #"deuterium isotope"#, #""^2H#; and a smaller few hydrogen nuclei contain 2 neutrons to give the #"tritium isotope"#, #""^3H#.
The atomic mass printed on the Periodic Table is the weighted average of the isotopes. And as #Z# grows larger, the isotopic distribution of a given element becomes correspondingly large.