Enter the phrase "vacuum leak" into your favorite internet search engine. For example, it took me about 3 seconds to find stuff like this:

https://www.samarins.com/glossary/vacuum-leaks.html

https://completecar.ca/maintenance/engine-vacuum-leak-symptoms/

Because your are compromising the manifold vacuum required to pull the air/fuel mixture into the cylinders.

Because air entering the intake manifold bypasses the Mass Air Flow (MAF) sensor.

In other words, the engine computer doesn't know about it, and cannot mix in the correct amount of fuel.

You're changing the correct/metered air/fuel mix ratio when you introduce more air into the intake by removing a vacuum hose. Now there's isn't enough fuel to compensate the extra air to make the mixture burn correctly thus causing poor combustion and therefore rough idle.

https://www.youtube.com/watch?v=SZSZLCKvRoo

At about 2 minutes 45 seconds into this video, Scotty discovers a big split in the rubber intake tubing & explains that the big vacuum leak happens past the computer sensor (MAF) that samples the incoming air & so the compter is giving the wrong amount of fuel to the mixture.

In an engine without a computer, the idle is set by screws on a carburator or injectors while the engine is idling. You turn the screws in or out until the idle is smooth. The same thing happens when a vacuum leak is introduced past the point of where fuel is added to the air, now the engine is starved of fuel because of additional air introduced by the vacuum. If the leak is small enough, you might be able to adjust it until it's smooth again. If the leak is big enough you might be able to hear it- makes a hissing sound.