。
Invite anyone who wants to come.
Literal
Come-want-[signs-of-feeling-がる]-[ing-ている] person [if-なら] anyone invite.
来たがっている uses the ~たがる suffix on the desiderative ~たい — '[someone else] shows signs of wanting'. The ~ている makes it an ongoing state. なら + 誰でも works as 'if [they are] anyone who wants.'