Dairy cows are normally dried off after a period of around 10 months in milk. At this point the udder isn't producing as much milk as at the start of lactation, so it's not so bad for the cow. The udder eventually stops producing milk. If the same thing happens during the peak months in lactation, the udder can get big and painful before it stops producing milk.
In response to the mastitis discussion, cows can get mastitis at any time of year, not just at drying off or during the dry period. Subclinical mastitis is a big problem among dairy herds today (the cows don't have any signs of infection, but the milk has an increased number of cells in it), with a significant proportion of the national milking herd having this. It's not fatal and commonly isn't any problem for the cow, just for the farmer whose cell counts have gone through the roof!.
Clinical mastitis (i.e. signs of infection) is quite common and it is the really scute cases that are potentially fatal. Many cases of clinical mastitis aren't though and the cow gets a hot, sore quarter that is easily dealt with.