The binomial theorem is a formula that provides a way to expand expressions that are raised to a power, specifically in the form of (a + b)^n. It states that this expression can be expanded into a sum involving terms of the form C(n, k) * a^(n-k) * b^k, where C(n, k) is a binomial coefficient representing the number of ways to choose k elements from n elements. The coefficients C(n, k) can be found in Pascal's triangle, which is a triangular array of numbers. Each number is the sum of the two directly above it. The binomial theorem is widely used in algebra, probability, and combinatorics, making it a fundamental concept in mathematics.