A Laurent polynomial in x (over a field k) is an expression of the form
where the coefficients ai lie in k. (You can take k to be the real numbers or complex numbers.)

For example, 10+5x, x-1, and x-2+3x2 are all Laurent polynomials.

They can be added and multiplied in just the way you expect (so that x.x-1=1) and the collection k[x,x-1] of all Laurent polynomials forms a commutative ring.