What is hafrashas challah?

It is the mitzvah of separating a small piece of dough when baking from a large enough batch. The piece is set aside and burned, and when the batch is big enough a bracha is said.

How much dough requires taking challah with a bracha?

It depends on the amount of flour, commonly around five pounds or more for a bracha, but the shiurim vary between poskim. Confirm the exact amounts with your rav.

Why do women say a tefillah when taking challah?

Taking challah is considered an eis ratzon, an opportune time for prayer, so many use the moment to daven, and keep a hafrashas challah card with the bracha nearby.