Okay kiddo, so there was a man named Kyllo who was suspected by the police of growing marijuana in his house. But instead of knocking on his door and asking if they could come in, the police used a special device called a thermal imaging camera to look at the outside of Kyllo's house and see if there was any heat coming from inside that might indicate he was growing marijuana.
Kyllo got upset and said the police should not be allowed to use the thermal imaging camera without a warrant. The case went all the way to the Supreme Court, which had to decide whether using this camera without a warrant violated Kyllo's Fourth Amendment right to be free from unreasonable search and seizure.
The court decided that it did violate his rights, because using the thermal imaging camera was like "looking inside" his house and seeing what he was doing without his permission. They said this was not okay, and the police needed to have a warrant signed by a judge in order to use this kind of technology to look inside someone's home.
So, in short, Kyllo v. United States was a case where the Supreme Court decided that the police can't use thermal imaging cameras to look inside someone's home without a warrant because it's like a form of spying and violates our Fourth Amendment rights.