What are the blue-backed cards in Dominion for?
The blue backed cards are the randomizer cards.  

They are listed among the contents (on page 2) and the main use is detailed on pg 5 of the rules.


  For example, the players can shuffle the
  Randomizer cards for all Kingdom cards and
  draw 10 to select the cards for the game. 
  
  Or,
  players can take turns selecting cards.
  Players may also use the Randomizer cards
  as Placeholders to mark the card piles so
  empty piles are easily seen.


A lot of folks use a random deck generator, we have a list here at B&amp;CG.  If you use sleeves, it may be helpful to use a different color sleeve for the randomizer cards so that they catch your eye easier.

Do not add them into the piles unless you want to change the balance of the game.  There are supposed to be 10 of each card, not 11. Some game strategies revolve around depleting piles fast or unexpectedly and you would impede those by having 11 cards in each stack.  Also, since they have a different back, they will be noticeable unless you are using opaque sleeves.