Expressions are combinations of numbers, variables, and operators that represent a value. They can be as simple as a single number, like 5, or more complex, such as 3x + 2. In mathematics, expressions are used to convey relationships and perform calculations without an equal sign. In programming, expressions are used to evaluate values and execute operations. For example, in the programming language Python, an expression like a + b calculates the sum of variables a and b. Understanding expressions is essential for solving problems in both math and coding.