The surplus of oxygen allowed amphibians, which take in some of the gas through their skins, to breathe more efficiently and grow to larger sizes. Arthropods breathe in a different way: they possess a network of branching tubes called tracheae that connect small openings in an invertebrate’s exoskeleton to its cells, and oxygen seeps through the body via this system. In an oxygen-rich atmosphere, more oxygen could be diffused through this branching network, and this opened up evolutionary pathways that allowed arthropods, too, to grow to gargantuan proportions. The fact that the oxygen would have increased the air pressure as well meant that the large flying insects of the time would have gotten more lift for each beat of their wings, allowing flying arthropods to reach sizes that are structurally impossible for their present-day relatives.
Read more: The History of Air | Science| Smithsonian Magazine