A space $X$ is locally path connected if $X$ has a basis of path connected open sets.
A follow-up to this question:
Hatcher Universal Covering Space Construction - Basis
From this definition, $X$ just has a basis of some collection of path connected open sets. Why can we actually take all path connected open sets to be a basis for $X$ when $X$ is locally path connected?
A basis for a given topology is just a collection of open sets $B$ such that every open set is a union of elements of $B$. This will remain true if you add more open sets to $B$. So, any collection of open sets which contains a basis is itself a basis.