I know that icing your heels on and off for 20 minutes help alleviates the pain associated with plantar fasciitis but I am curious how it helps exactly...

Low temperature help to reduce inflammation so all the symptoms of inflammation are reduced too including swelling redness and of course pain. You can find more info in a good website I use for my plantar fasciitis : http://www.plantar-fasciitis-elrofeet.com