The smoke from the fire was so thick that people started choking and gasping for air.

choking 是动词 choke 的现在分词形式。choke 本意是“窒息、呛住”，指呼吸道被阻塞或受到刺激而无法正常呼吸。在句中，choking 描述的是人们因浓烟而呛咳、呼吸困难的状态。