Stardollars are a currency used on Stardoll. Stardollars can be obtained from a superstar membership, buying them seperately , by doing tasks in Stardoll Academy or by selling something at your shop (called a StarBazaar) Players can buy things with this money, such as clothes, makeup, jewllery or things for their suite,etc. You cannot literally "give" money to other players, like on some other sites where you can just hand people money, but you can buy them gifts or buy something they are selling.
Stardollars are circular gold like coins that have a number one (1) placed in the middle.
At the very first Stardollars were the only currency avaible on Stardoll. By that time you could get them by buying a superstar membership and selling things in your bazar if you were superstar. If you were non-superstar you get 1 daily stardollar and more four by playing Play & Earn. You could keep the one but you would have to spend the other four ones ( only on non superstar itens).
Later Starcoins appear and Stardollars were block as only superstar could use them.
In the present you can have acess to stardollars without being a superstar as well now almost every item on starplazza it's free for everyone to buy ( unless special stores like Royalty, LE, Antidote, Young Hollywood,...)