The early atmosphere had almost no oxygen. Oxygen appeared because of living organisms. About 2.7 billion years ago, algae (and later plants) began to carry out photosynthesis, which uses carbon dioxide and water and releases oxygen.
The word equation is: carbon dioxide + water → glucose + oxygen. This did two things at once. It removed carbon dioxide from the atmosphere and it added oxygen to it.
The change was slow. Over hundreds of millions of years the oxygen level rose. Some of the oxygen reacted with other substances at first, such as dissolved iron, so it did not build up straight away. Later, as plants spread across the land, the oxygen level reached the 21% we have today. Oxygen also formed the ozone layer, which absorbs harmful ultraviolet radiation and made it safer for more complex life to develop.
The time scales are huge, so scientists use orders of magnitude and large numbers such as billions of years when they describe these changes.