A variable is some attribute that describes something (ie. a person, place, thing, or idea). The value of this variable can "vary" between entities. For example a variable of a person could be their hair or eye colour, which can take different values for different peoples.
Variables can be classified into a few different categories and sub categories depending on the forms they take.
Qualitative variables are any variables in which their values belong to a category, instead of a magnitude.
Examples:
Quantitative variables are any variables in which their values take on numerical values that represent different magnitudes of a variable.
A quantitative variable is considered discrete if it's possible values form a set of separate numbers (ie. natural numbers or integers)
Examples:
A quantitative variable is considered continuous if it's possible values form an interval (ie. the reals between 3 and 4).
Examples: