Search and seizure would mean something like the government taking your cell phone and going through every message you've ever sent, or entering your home and searching through all your dresser drawers. They need to have a court-approved reasonable cause for doing something that invasive.
Quartering of soldiers would mean soldiers would have the right to enter your home and expect you to provide them food and lodging. That's pretty invasive too.
In either case, we're talking about invasions of your privacy, your personal space. Court justices have used statements like those about search and seizure and quartering of soldiers to show that the constitution does give attention to citizen's right to privacy, even if not using the exact term "right to privacy."
