Sections of a vector bundle are locally vector valued

Question

Can someone explain to me what it means to say that "the sections of a vector bundle are locally vector valued". Does it mean that for every point $x\in X$ , the base space, there is a neighbourhood $U$ containing $x$ such that under the local trivialisation of $U$, i.e. when the section $s\restriction_U$ is conjugated by the isomorphism trivialising $p^{-1}(U)$, it takes the same vector value for all $x\in U$.