There are two forms of respiration, Aerobic and Anaerobic

Aerobic respiration uses Oxygen and Anaerobic respiration does not use Oxygen

Plants and Animals all must respire in order to convert their food into energy so they can grow and move. These living things use oxygen in their respiration, therefore Plants and Animals carry out Aerobic Respiration.

Bacteria can respire without oxygen Anaerobically. It was these bacteria that provided the planet Earth with all the Oxygen, all the plants and animals require. Even now bacteria can respire without Oxygen, it is these bacteria that live in your gut, that make Milk go off.

The Word Equation for Aerobic respiration

Glucose + Oxygen → Carbon Dioxide + Water + energy