Context: Let $M$ be a compact, connected, edgeless bidimensional differentiable manifold and let $f:\mathbb R\times M\to M$ be a flow of class $C^2$ in $M$.
What does it mean that a flow has no singularities? I understand that a vector field does not have singularities but I do not understand the flow... or is it that we can trivially associate a vector field with a flow?