Tardigrades were microscopic creatures on Earth. There were trillions of them on Earth. They lived in the air and in the water, capable of surviving the coldest temperatures and living almost forever.
To explain them to Clara Oswald, the Eleventh Doctor got her to stare at the TARDIS column for ten seconds, then shut her eyes, count to five, and open them again. All she saw were those "tiny little things that float in front of your eyes when you look at a bright light". She hypothesised that this was just fluid being reflected back, but the Doctor corrected her.
In 2013, Clara taught about tardigrades to her Coal Hill School English class, including Courtney Woods, Joshua Adams, Zehra Jalindra, Mackenzie Brooks, Liam Mannings, Chiana Holden, Tommy Breare, Kelly Squires and Sam Kaye-Jones. They went outdoors for this lesson. She gave her students much the same instructions as the Doctor did her, except to look at the sky. (PROSE: Normality)