Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term") ... so it says "many terms".
A polynomial can have:
constants (like 3, -20, or ½)
or
variables (like x and y)
or exponents (like the 2 in y^2),
but only 0, 1, 2, 3, ... etc are allowed
Wiki says,
In mathematics, a polynomial is an expression consisting of variables and coefficients which only employs the operations of addition, subtraction, multiplication, and non-negative integer exponents. An example of a polynomial of a single variable x is x2 − 4x + 7. An example in three variables is x3 + 2xyz2 − yz + 1.