It is a black variant of lemonade that is made from Squidward's ink.
Role in episode
Patrick continuously scares Squidward after discovering that he produces ink when he's scared, and sells it with his lemonade.
Squidward does not want to give any more ink to Patrick, so the latter resorts to scaring the former, including revealing his inner organs and letting a spider named Mildred enter Squidward's house. Squidward sprays a lot of ink out of his nose and Patrick brings the black lemonade outside to sell at the lemonade stand.
Patrick's final plan is to make a haunted area in front of Squidward's house, causing the now-paranoid Squidward to spray a lot of ink. Eventually, he runs out of the haunted zone and finds out that SpongeBob and Patrick were using his ink to sell lemonade the whole time.
Unfortunately, Squidward is unable to make more lemonade, so he chooses to have a customer scare him in order to get lemonade. Don the Whale does, and Squidward sprays ink like crazy all over the customers. Eventually, the customers find out the "source" and puke in Squidward's house.
SpongeBob and Patrick decide to move out of the lemonade business to sell cookies. As Squidward eats one of them, SpongeBob and Patrick say they used spider eggs as chips, resulting in Squidward screaming out spiders and spraying ink as the episode ends.
It is actually possible to make black lemonade in real life by coloring it black using activated charcoal, a tasteless compound known to have various health benefits.
Cephalopod ink can actually can be put on other foods, with pizza and pasta being major examples.