At an Irish wedding, the father of the bride gives away his daughter. At an Irish funeral, the bride's father is given away.
This darkly humorous one-liner plays on the stereotype of heavy drinking at Irish wakes. The "giving away" at a wedding is a ceremonial handoff; at a funeral, it implies the father has drunk himself into a state requiring transport home—or, more morbidly, that he's the next to be buried. It's a joke, not a cultural fact.