What is meant by phase, phase difference, in (and out of) phase in wave terminology?

What is meant by phase, phase difference, in (and out of) phase in wave terminology? How do you get the relation

$$y=A\sin(\omega t + \phi)?$$
Since the graph of sin function is identical to that of a sin wave, I know why the sine function is used in the wave equation, but how do you get $\omega t + \phi$ as the sine angle?