Now we're getting into linguistics with the question of "what is a wave?"
In quantum physics, basically everything is waves, in the sense that the same mathematical formulae used to describe waves are used to describe quantum phenomena. The intuitive human-scale dynamics of waves don't necessarily apply though.
For example, sound waves can't propagate through a vacuum, but light waves can. Aside from that, they follow mostly the same rules. You can use the same math the describe interference of sound waves and light waves, for example.
People talk about the "particle/wave duality" of photons because in some ways they behave like waves and in some ways they behave like particles. But both of those words are stretched a little from their everyday plain-english usage, and the precise reality would require years of study to understand.
Plain English wasn't made to be that precise or objective. That's why we use math. :)
I'm no expert in quantum physics so take this all with a grain of salt.