I'm having trouble understanding the intuition of the moving average model. How does summing up a bunch of white noises related to predicting your particular time series data?

Suppose I have a MA(q) model $y_t = \mu + \epsilon_t + \theta_1 \epsilon_{t-1} + ... + \theta_q \epsilon_{t-q}$, where do these $\epsilon's$ come from? How does one estimate these $\epsilon's$?