It's a vivid imagery, conjuring up the sound of water rushing down a drain, hence the boisterous and unrestrained laughter.
Here are some examples of how it's used:
* "He told such a funny joke, I just started laughing like a drain."
* "The kids were laughing like a drain at the clown's antics."
It's a casual and informal phrase, often used to describe a hearty and infectious laughter.