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`If the name is neither a shell function nor a builtin, and contains
no slashes, bash searches each element of the PATH for a directory
containing an  executable  file  by  that name.  Bash uses a hash
table to remember the full pathnames of executable files.  A full
search of the directories in PATH is performed only if the command is
not found in the hash table.`

I interpret that to mean if you call foo from /a/b/c then it
1) looks for /a/foo
2) looks for /a/b/foo
3) looks for /a/b/c/foo
4) iterates through $PATH, in order, looking for the first executable foo.


Colin