Hi!

They're probably PIH - Post inflammatory hyper-pigmentation. They're red marks left behind from spots you've had in the past. Most of the time they fade over time, but I have been told that the more stubborn ones could be broken blood vessels? I'm not sure that's 100% true though. There's a whole board for people trying to get rid of them:
http://www.acne.org/...eft-after-acne/Natural things that could help are: Lemon juice, Apple Cider Vinegar, Aloe Vera, Tumeric etc. These may take some time to fade them though. There are topics on the above board about where to get the ingredients and how to apply etc.
If they're more stubborn and you want faster results, I guess you could try IPL treatments/chemical peels, but it's reeaaally important you do your research beforehand. Choose a reputable place that does those procedures.
Hope this helps!