What does Rivka mean when she says this quote to Hannah in The Devil's Arithmetic?"A taker is not a giver. And a giver is not a taker either. ...

Rivka is expressing the idea that each of us is a giver and a taker at different times in our lives.  It is not good to lock ourselves in to being one or the other, because if we are always takers, we never give, and if we are always givers, we never take.  Giving thanks to someone for something given is kind, but it should not be the focus of our lives.  We should concentrate instead on being both givers and takers, making sure that we express our thanks for what we take by "hand(ing) it on", becoming a giver for someone else.

Rivka says these words to Hannah when she gets Hannah a coveted job in the kitchen, and she tells Hannah that she learned the philosophy behind them from her mother, who is no longer living.  The words are especially important in the context of the camps.  Survival in the camps depends on a different set of rules than those which govern ordinary life.  In order to make it, a person must learn some hard and counterintuitive lessons, lessons which might at times seem contrary to a basic sense of humanity, such as quickly accepting that some who are too far gone cannot be saved, to know "when to fight and when not to", and to know "who to talk to and who to avoid".  The inmates of the camp are vitally dependent on each other.  Though it is important to retain the capacity to be a giver, in the interest of survival in a world gone crazy, it is equally vital to learn to be a taker at times as well.