A fibre map is a map of topological spaces $f: E \rightarrow B$ for which there exists a space $F$ such that any point of $B$ is contained in some neighbourhood $U$ satisfying the following: on $f^{-1}U$ $f$ restricts to the natural projection $F \times U \rightarrow U$ via some homeomorphic identification of $f^{-1}U$ with $F \times U$

One class of examples are covering maps. Another example is the map $SO_3 \rightarrow S^2$ sending a rotation to the point it sends the ``North Pole'' to.