Dear Ducklet Cat:
Hook= fishing hook
Line= fishing line (to which the hool is attached)
Sinker= a heavy (often lead) object attached to the fishing line which keeps it and the hook from floating on the water
So, when someone 'swallows' information 'hook, line and sinker,' she believes it without reservation, as you say. It is often used to describe uncritical belief.
I hope this is helpful,
Interested in Language