Scientists who believed the Miasma Theory claimed many diseases were spread by pollution/bad air quality. When microscopes were invented, they analyzed the germs and concluded germs from water and other surfaces caused the majority of diseases.
Robert Koch grew this bacteria and isolated the microorganisms from sheep, he injected the bacteria into the mice. They became sick with anthrax (the organisms in the sheep).
If germs were the cause of anthrax then germs from sick sheep could make mice sick.