I know that the pi is like a summation except multiplication instead of addition and that P(x) means the probability of, but I'm having trouble putting it all together, esp the $w_i$ such that $w_1, w_2, ..., w_{i-1}$. If anyone could express this equation in english, I'd be really grateful $:)$
The comma is just a list separator. A listing of events in the probability function is interpreted as the intersection of those events. So $P(A,B)$ is the probability of $A$ and $B$ both occurring. Also expressed as $P(A \cap B)$
The pipes refers to conditional probability. So $P(A\mid B)$ is the probability of $A$ occurring when it is given that $B$ has occurred.
Putting this together, $P(\omega_i \mid \omega_1, \omega_2, \ldots , \omega_{i-1})$ reads: the conditional probability of event $\omega_i$ given the occurrence of events $\omega_1$ and $\omega_2$ and so on to $\omega_{i-1}$.
$$P(W) = \sum_{i=1}^n P(\omega_i \mid \omega_1, \omega_2, \ldots , \omega_{i-1}) \\= P(\omega_1)\cdot P(\omega_2 \mid \omega_1)\cdots P(\omega_n \mid \omega_1, \omega_2, \ldots , \omega_{n-1})$$
The probability of the first event, times the probability of the second given the first, times, et cetera up to, times the probability of the $n^{th}$ event given all the previous events.