Antioxidants are like little soilders in our body, witch are either nutrients(like vitamins or minerals) or enzymes(these proteins that help with the chemical processes in our body).
Almost every chemical process our body does (digestion, breathing, etc.) releases these things called "free radicals", witch our harmful to and hurt our cells and DNA. This happens because our chemical processes take away pieces of these radicals, therefore they are short of electrons and steal them from our cells/DNA, witch damages them.
It is impossible to completely prevent this, although antioxidants help by making those free radicals "neutral". However, when they do this, the antioxidant itself gives it's own parts, so that is why we constantly have to get more and more antioxidants-the ones that have already done their job become useless.
Like with everything, too much of a good thing isn't good, and if we take in too much of these they will cause side-affects. This is why FDA still isn't sure about supplements, and not everyone recommends that you take them.
Different types of antioxidants are needed to neutralize different free radicals, and are found in different places.
Pretty much, what all of this means, is that the berries we've mentioned have a lot of good vitamins and minerals, and many of witch are specifically designed to aid our immune system.
Hope I explained this well. :]