Swallow a gudgeon/gudgen

...Hook, line and sinker.

What is meant by the above and under what circunstances is the phrease used?

"...swallowed (the falsehood/story/tall tale) hook, line and sinker"
means that
the listener is extremely guillible

Hook, line and sinker are all fishing equipment. The object of the angler is to persuade the fish to swallow the bait or artificial lure which contains the hook. Similarly, a person may be persuaded to believe (or swallow) an artificial story.

"...This phrase originated in the United States about the middle of the 19th century, but a much older English phrase (to swallow a gudgeon) embodied the same idea. A gudgeon is a small fish used for bait. John Lyly in 'Euphues' writes: 'You have made both me and Philautus to swallow a Gudgen.'" From The Dictionary of Cliches by James Rogers (Ballantine Books, New York, 1985).