Smooth varieties are a concept in algebraic geometry, referring to certain types of geometric objects called varieties. A variety is considered smooth if it has no singular points, meaning that locally around any point, it resembles Euclidean space. This property is important because smooth varieties have well-defined tangent spaces, making them easier to study and understand. In the context of algebraic geometry, smooth varieties often arise in the study of polynomial equations. They play a crucial role in various mathematical theories, including intersection theory and moduli spaces. The smoothness condition ensures that many desirable properties hold, facilitating the application of tools from differential geometry and topology.