There's actually lots of different kinds of solids in the air we breathe. The oxygen, nitrogen, carbon dioxide, etc. But there are lots of other things that float around in the air. For example, if you've ever looked at the air just the right way into the sunlight, you've probably seen dust floating around.
Dust is a solid that's made up of lots of other kinds of solids.
You may have had friends who are allergic to pollen in the air. Pollen is a solid that comes from plants during the spring and summertime. There's also all sorts of bacteria and viruses in the air - this is an easy way to catch a cold if you're around someone else who has one. Little tiny bits of dirt and rocks and whatnot float up into the air off of the ground. And anywhere that there's people or animals, there's bound to be a whole lot of dead skin cells in the air that are rubbed off of people's skin every day.