Antioxidants control or stabilize free radicals, which are responsible for a great deal of damage within the body.
These free radicals are destabilized because they lack an electron.

In seeking to stabilize themselves, they attack other molecules in an effort to take what they need from them, which results in those molecules becoming destabilized as well.

If a cell accumulates enough free radicals, cellular damage can occur, which can lead to tissue damage as the free radicals roam, increasing their population.   More detail...