p-adic geometry is a branch of mathematics that studies geometric structures using the p-adic numbers, which are a system of numbers that extend the usual integers and rational numbers. These numbers are defined based on a prime number p and provide a different way to measure distances, leading to unique properties in geometry. In p-adic geometry, objects like curves and surfaces are analyzed in a way that emphasizes their behavior under p-adic valuations. This approach allows mathematicians to explore connections between algebra, number theory, and geometry, revealing insights that are often hidden in classical settings.