A zeta function is a special type of mathematical function that encodes information about the distribution of prime numbers. The most famous example is the Riemann zeta function, which is defined for complex numbers and has deep connections to number theory. It plays a crucial role in understanding the distribution of primes through its relationship with the Prime Number Theorem. Zeta functions can also be generalized to other areas of mathematics, such as geometry and algebra. For instance, the Dedekind zeta function is associated with number fields and helps in studying their properties. Overall, zeta functions are powerful tools that reveal insights across various mathematical disciplines.