Categorical data is a collection of information that is divided into groups. I.e, if an organisation or agency is trying to get a biodata of its employees, the resulting data is referred to as categorical. This data is called categorical because it may be grouped according to the variables present in the biodata such as sex, state of residence, etc.
Categorical data can take on numerical values (such as "1" indicating Yes and " 2 " indicating No), but those numbers don't have mathematical meaning. One can neither add them together nor subtract them from each other.