Animal cells need food and water and air with oxygen in it. We don't know exactly what needs to be in the food for animal cells, so usually animal cells are grown in food that has some blood serum in it. Blood serum is blood without any red or white blood cells. Animal cells grown in food without any blood serum grow only very slowly. The blood serum is a complicated part of the food, with lots of kinds of molecules in it, different from vitamins and minerals and purified proteins and such.

Also, animal cells need some way to get their waste products away from them. When growing animal cells in the lab, scientists usually take away the liquid on the cells after it has too many waste products and too little food, and they put fresh liquid food on the cells every few days. Animal cells in the lab are often grown in flat dishes called Petri plates, and the cells stick to the dishes.

Some animal cells grow in their liquid food without sticking to the surface of the container. In that case, they can be transferred to a bigger container with fresh food when there are too many waste products and too little food.

Here's the website for the article I read about how we still can't grow animal cells very well without blood serum:

animal and cell culture