Taxation is the act of governments/sovereigns collecting money from individuals and businesses. This money is then used to provide for all the state-run systems, services and benefits.
Why do taxes exist?
The root of taxation lies in the Social contract. In social contract, we forego some of our freedom in order to gain some rights including safety of life and caring for each other.
Crudely speaking, you and I are foregoing our right to murder each other in order to ensure safety of our lives. Therefore, murder becomes a crime as per law, and state controls enforcement of the law.
Social contracts establish a form of authority. That authority needs some financial input in order to cater to individuals’ rights as per the social contract. i.e. to ensure safety for all; to build roads, hospitals and schools; and so on. This financial input is what you and I call tax, and the process of defining, computing and collecting this is taxation.