To get to the "other side". It's a pun. (I honestly didn't get this for most of my life.)
Seems it's typical American humor. Probably trying to play on the absurd side of humor. Never found that super funny. It's very cultural I guess.
But it can do derivative humor. Exemple: How many Alzheimer patients you need to change a light bulb? Answer: To get to the other side.
I don't know about typical. It's considered a very bad joke here, something only repeated to make fun of how bad the joke is. For example, a lazy writer might use it to represent how bad a comedian a character is.
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