Calculated variables are variables based on a formula, they do not get stored on respondent level but instead are calculated on the fly each time a value is requested. Calculated variables can have any of the base data types (numeric, text and date).
Calculated variables can be very easy in situations where data is added or changed to a dataset on a regular basis as you do not need to(re)run any scripts to update the values of these columns.
If for example your questionnaire asks for your respondents age in years, you can recorde that age into categories and when a new respondent is added to your dataset the categorization is available immediately.
This makes it much easier to manage your dataset, and allows these types of recodes to be applied automatically when the dataset is used in an online environment where data is added in near real-time.