Defintion:
Suppose $I$ is a set and for every $i\in I$ there is a set $M_i$. Then the infinitary intersection is defined as follows: $$ \bigcap_{i\in I}M_i:=\{x :x\in M_i \text{ for every } i\in I\} $$
I tried constructing a simple example to visualize the definition. Hence let $I:=\{1,2,3\}$ and for every $i\in I$ there is a set $M_i$, so all in all we have $M_1, M_2, M_3$. Would $\bigcap_{i\in I}M_i=M_1\cap M_2 \cap M_3$?
Yes, you are right.
Try to imagine what is $$\bigcap_{n\in\Bbb N}\left(-\frac{1}{n},1+\frac{1}{n}\right)$$