Chemical symbols are the abbreviations used to denote the elements, like a short form.
Every element are denoted by its chemical symbol in a chemical formula of a compound.
Generally first letter(capital letter) of the element is used to represent its symbol of it. for example, H for hydrogen, O for Oxygen, etc.
If two or more elements have the same first letter, then the first letter is followed by the next non-repeating letter is used as a chemical symbol. For example, chlorine, and cadmium, both have the first letter as C so it is followed by the next non-repeating letter(small letter) such as Cl for chlorine and Cd for cadmium.
Sometimes, the symbol is derived from its Latin name also. For example, sodium, its symbol is Na derived from its Latin name.