GRE stands for Graduate Record Exam.
Many graduate math programs require or recommend taking the GRE Math Subject Exam for admission to their department. There is also a GRE General Exam that may be required, which is different, and less important (it is similar to the SAT test).
Here is some old descriptive info from 2012: The Math Subject exam is 2 hours and 50 minutes long, and it consists of approximately 66 multiple-choice questions drawn from courses commonly offered at the undergraduate level.
Calculus – 50%: Material learned in the usual sequence of elementary calculus courses—differential and integral calculus of one and of several variables—includes calculus-based applications and connections with coordinate geometry, trigonometry, differential equuations, and other branches of mathematics.
Algebra – 25%: Elementary algebra: basic algebraic techniques and manipulations acquired in high school and used throughout mathematics. Linear Algebra: matrix algebra, systems of linear equations, vector spaces, linear transformations, characteristic polynomials, and eigenvalues and eigenvectors. Abstract algebra and number theory: elementary group theory, rings and modules, field theory, and elementary number theory.
Additional Topics – 25%: Introductory real analysis: sequences and series of numbers and functions, continuity, differentiability and integrability, and elementary topology of R and R^n. Discrete math: logic, set theory, combinatorics, graph theory, and algorithms. General topology, geometry, complex variables, probability and statistics, and numerical analysis.
GRE general test info (verbal and quant), including free study material.
GRE subject exam info: you might search for:
GRE subject exam sample (former students have recommended this study guide):
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. There was a discussion entry there about finding past GRE math subject exam questions to practice on: http://math.stackexchange.com/questions/5892/gre-past-papers