"Her First Ball" is told from the perspective of a third person narrator; this is the point of view. The third person narrator describes the sights and sounds of the ball in detail and this omniscient ("all knowing") narrator also gives the reader insight into Leila's thoughts and emotions as she attends her first ball. Therefore, the writer gives the reader a point of view that is over and above all the events in the story but the narrator can also pry into Leila's thoughts. For example, we know that Leila is trying not to let on (to the Sheridan girls) that she is very excited; so, outwardly, she's remaining relatively calm, but inside she's bursting with excitement.
As the night goes on, the reader sees Leila's experience from an outside or objective perspective as well as an internal or subjective perspective. The reader gets the perspective of both worlds from this omniscient third person point of view. We (readers) get both perspectives in the last line as well, noting the scene overall as well as Leila's emotional/internal transformation from excited to gloomy to excited again:
The lights, the azaleas, the dresses, the pink faces, the velvet chairs, all became one beautiful flying wheel. And when her next partner bumped her into the fat man and he said, "Pardon," she smiled at him more radiantly than ever. She didn't even recognise him again.