The process you're referring to is called decomposition reaction. During this reaction, a single compound breaks down into two or more simpler compounds. In the case of hydrogen peroxide, the decomposition reaction can be represented as:

2H2O2 (Hydrogen Peroxide) → 2H2O (Water) + O2 (Oxygen Gas)

In this reaction, hydrogen peroxide breaks down into water and oxygen gas. The oxygen atoms from hydrogen peroxide combine with hydrogen atoms to form water molecules, while the remaining oxygen atoms form oxygen gas. This reaction is often catalyzed by enzymes or certain metal ions, such as manganese or iron, which speed up the process without being consumed in the reaction.