variable is an alphabetic character representing a number, called the value of the variable, which is either arbitrary or not fully specified or unknown. Making algebraic computations with variables as if they were explicit numbers allows one to solve a range of problems in a single computation. A typical example is thequadratic formula, which allows one to solve every quadratic equation by simply substituting the numeric values of the coefficients of the given equation to the variables that represent them.
The concept of variable is also fundamental in calculus. Typically, a function y = f(x) involves two variables, y and x, representing respectively the value and the argument of the function. The term "variable" comes from the fact that, when the argument (also called the "variable of the function") varies, then the value varies accordingly.
In more advanced mathematics, a variable is a symbol that denotes a mathematical object, which could be a number, a vector, a matrix, or even a function. In this case, the original property of "variability" of a variable is not kept (except, sometimes, for informal explanations).
Similarly, in computer science, a variable is a name (commonly an alphabetic character or a word) representing some value represented in computer memory. In mathematical logic, a variable is either a symbol representing an unspecified term of the theory, or a basic object of the theory, which is manipulated without referring to its possible intuitive interpretation.