When you dissect it, it dies.
Get it? Just like a frog dies when you dissect it, so does a joke when you explain it.
Basically, the frog is used as an analogy, to help people understand that jokes shouldn't be explained, because the joke will die, or more specifically, become unfunny. So, just like when a frog dies when you dissect it, so does a joke when you dissect, or explain it.
Edit: /u/elliot91 caught me out on my shameless [copy paste](https://www.reddit.com/r/Jokes/comments/2pcec3/a_joke_is_like_a_frog/). All my upvotes are belong to him.
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