In algebraic geometry, a morphism f : X → S {\displaystyle f:X\to S} between schemes is said to be smooth if it is locally of finite presentation it is flat, and for every geometric point s ¯ → S {\displaystyle {\overline {s}}\to S} the fiber X s ¯ = X × S s ¯ {\displaystyle X_{\overline {s}}=X\times _{S}{\overline {s}}} is regular. means that each geometric fiber of f is a nonsingular variety. Wikipedia