Page "Section (fiber bundle)" Paragraph 13

For example, when E is a vector bundle a section of E is an element of the vector space E < sub > x </ sub > lying over each point x ∈ B.

In particular, a vector field on a smooth manifold M is a choice of tangent vector at each point of M: this is a section of the tangent bundle of M. Likewise, a 1-form on M is a section of the cotangent bundle.