The notation "R[x, y]" represents a polynomial ring in two variables, x and y, over a ring R. This means that the elements of R[x, y] are polynomials that can be expressed as combinations of powers of x and y with coefficients from the ring R. In this context, polynomials can include terms like a*x^m*y^n, where a is a coefficient from R, and m and n are non-negative integers. The structure of R[x, y] allows for various algebraic operations, such as addition and multiplication, making it a fundamental concept in algebra and algebraic geometry.