The paths in `$PATH` are searched in order. This allows you to override a system default with:
export PATH=$HOME/bin:$PATH
`$HOME/bin` is now the _first_ (highest priority) path. You did it the other way around, making it the _last_ (lowest priority) path. When the shell goes looking, it uses the first match it finds.
In case it's not clear, this all works by concatenating strings. An analogy:
WORD=bar
WORD=foo$WORD
`$WORD` is now `foobar`. The `:` used with `$PATH` is literal, which you can see with `echo $PATH`.