I'm going through Graph Theory by Reinhard Diestel, which defines an $H$-path as follows:
Given a graph $H$, we call $P$ an $H$-path if $P$ is non-trivial and meets $H$ exactly in its ends. In particular, the edge of any $H$-path of length $1$ is never an edge of $H$.
Please could somebody help me understand what this means?
You can think of $P$ and $H$ as being subgraphs of a larger graph. Here's another version of what I think is intended by Diestel there:
If $H$ is a subgraph of $G$, then a path $P$ in $G$ is an $H$-path if the endpoints of $P$ are in $H$ and none of the other vertices or edges are in $H$.