Oxidative theories of aging place the blame for the damage of aging on reactive oxidizing molecules, generated most notably in the mitochondria of your cells, and which tend to break the protein machinery they react with. Oxidative stress is the term given to ongoing damage (and efforts to repair it) caused by the presence of oxidative molecules in and around cells. Levels of oxidative stress can alter as a result of heat, exposure to ionizing radiation, the details of diet, and all sorts of other environmental influences.
The relationship between oxidative stress and the pace of aging is far from straightforward, however. There is more oxidative stress with age, but this is an expected result of carrying a high level of cellular and molecular damage. Some very long-lived species, such as naked mole rats, show very high levels of oxidative stress but don't appear to be particularly harmed by it. Mild oxidative stress can be beneficial, triggering increased cellular maintenance for a time to produce a net benefit. Oxidative compounds are also widely used in our biochemistry for necessary signaling purposes.
You can see the nature of this complex relationship between oxidative stress and aging by looking at what happens in interventions that reliably slow aging and extend life, such as calorie restriction in rodents:
Oxidative stress is observed during aging and in numerous age-related diseases. Dietary restriction (DR) is a regimen that protects against disease and extends lifespan in multiple species. However, it is unknown how DR mediates its protective effects. One prominent and consistent effect of DR in a number of systems is the ability to reduce oxidative stress and damage. The purpose of this review is to comprehensively examine the hypothesis that dietary restriction reduces oxidative stress in rodents by decreasing reactive oxygen species (ROS) production and increasing antioxidant enzyme activity, leading to an overall reduction of oxidative damage to macromolecules.
The literature reveals that the effects of DR on oxidative stress are complex and likely influenced by a variety of factors, including sex, species, tissue examined, types of ROS and antioxidant enzymes examined, and duration of DR. [In] a majority of studies, dietary restriction had little effect on mitochondrial ROS production or antioxidant activity. On the other hand, DR decreased oxidative damage in the majority of cases. Although the effects of DR on endogenous antioxidants are mixed, we find that glutathione levels are the most likely antioxidant to be increased by dietary restriction, which supports the emerging redox-stress hypothesis of aging.
While thinking about antioxidants and their effect on aging, it's important to remember that location matters immensely. Ingested antioxidants of the sort you can buy in the store are convincingly demonstrated to do nothing for your health, and there is evidence to suggest that they are actually mildly harmful - for example by blocking some of the oxidant-based signaling mechanisms the body uses to dial up cellular housekeeping and muscle growth responses after exercise. Meanwhile researchers are demonstrating benefits in mice by targeting designed antioxidant compounds to the mitochondria in cells, the place that most oxidants are generated. Those antioxidants are not yet available for the rest of us, however. The antioxidant pills from the store don't deliver their contents to your mitochondria, and are thus not terribly helpful.