In my Discrete Structures class we covered the Principle of Inclusion and Exclusion. The formula that we looked at is:

$$\left | \bigcup\_{i = 1}^n A\_i \right |= \sum\_{r=1}^n \left( (-1)^{r-1} \sum\_{\mathcal{L} \subseteq [n]:|\mathcal{L}|=r } \left | \bigcap\_{j \in \mathcal{L}} A\_j\right | \right)$$

I understand what the overall formula means, however I would like to know what each of these terms mean. I understand the left side:

$\left | \bigcup\_{i = 1}^n A\_i \right | = \left | A\_1 \cup A\_2 \cup \ ... \cup A\_n\right |$
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However, the right side is a bit tricky for me to fully understand. If you can explain, in a simple one-liner, what each one of the terms (especially the squiggly L symbol) mean, it would be great.