variable
A variable is a placeholder — a labelled box that a number can be dropped into. We write a letter such as x, y, or t, and agree that it stands for some number. The number it stands for may be unknown (something we are trying to find), or it may be allowed to roam over many values (as when x sweeps across a graph).
Using a letter instead of a definite number is what lets algebra speak in general. The expression “2x” means “twice whatever number x is,” so it describes doubling for every input at once. Once we decide on, or discover, a particular number for x, we can substitute it back in and compute an ordinary numerical answer.
By long convention, letters near the end of the alphabet (x, y, z) are used for variables and unknowns, while letters near the beginning (a, b, c) are used for constants and fixed parameters — a habit we owe to Descartes. The convention is helpful but not a law; any letter can play any role if you say so clearly.
In the area formula A = l × w, the letters l and w are variables: each can take any positive length, and A changes with them.
Same formula, infinitely many rectangles — that is the power of a variable.
A variable is not a single secret number waiting to be unmasked; depending on context it can be one specific unknown (in an equation) or a quantity free to vary (in a function or formula).