Oxidative stress in cells produce peroxide and free radicals that could damage the cell. If your cells are damage, that is bad for you! Your organs will have errors in the transcription of the DNA. And then your cells will have 2 options die that is bad, or multiply without control that is worst (cancer). If you eat antioxidants with your diet, you'll minimize the oxidative stress of your cells so, your cells will be happy.
Oxidative stress is the bad part of being alive and breath oxigen hehe.
It is like the iron if you don't prevent oxidation with some special painting it will break, if you paint it with some especial pintures. Its durability will increase. So your pomegranate and other fruits and vegetables are your special pinture