The waves come from synchronicity of neurons "firing". When neurons fire there is a flow of ions that causes a potential difference. If a lot of this happens at the same time with some periodicity you can measure this. But it would be like looking at a CPU running some math operations and determining "there is periodic activity in the ALU" (which could be due to memory reads). Now this is a poor analogy because a single neuron doesn't do "one thing" it's massively distributed. My go to argumentation for "how the brain works" (and thus consciousness) has been that it's a massive coincidence detector that tries to encode these coincidences in spike train activity using spike train dependent plasticity. In doing so the brain echoes the coincidences of the neural (sensory) input, and since these encode for some "real" cause-effect you can predict the future: memory is "echoing" in a neural substrate, consciousness is exploiting those "echos" to try to predict the future. I wrote it up in 2011 https://www.dropbox.com/s/huol1vf4j1fs1ll/mind_matters.pdf?d... I've never seen anyone poke holes in this, and even hints at the details of this paper. Guess I chose the wrong career somewhere.