The sentence "Her fingers were busy telling the beads of her rosary" describes someone who is likely praying using a rosary. The rosary is a string of beads used in some religions, most notably Catholicism, to count prayers.

"Telling the beads" means that the person is moving their fingers along the beads of the rosary as they recite prayers. This suggests a state of devotion, contemplation, or seeking comfort through prayer.