A union of two events is when events happen, regardless on which side, and then counting those events the union is like a group of all events. All events that happened are put together into a union of events. Anything that happened in two groups falls into the domain of the union.
An intersection of two events is when only those events that happened in both groups are counted. If you use a venn diagram, you can see that for example if you have in group A = abc, and in group B = cde, the intersection is the event c because it appears in both groups.
