A variable measures an attribute (such as height, temparature, etc.) and assigns the measured state to a value. All measured values belong to a variable and an observation. An observation contains all values that were measured on the same object (such as student, item produced etc.)
The R community calls a data settidy if each variable is stored in a column, each observation is stored in a row and each type of observational unit forms a table (Hadley Wickham).
This structure somewhat corresponds to Codd's 3rd normal form.
Categorization:
Discrete vs continuous variables
Qualitative vs quantitative variables
Discrete variables can only take on a finite number of values.