It simply means two angles which are equal and which are made by the same lines. You must realize that two parallel lines are aligned the same way with its counterpart. So if another line crosses it, the angles made by it are going to be same.
More Corresponding Angles
The Internal Angles
In parallel lines the internal angles add up to 180 but again you do not need to memorize this. What we suggest is that whenever there are parallel lines identify two things
1. Corresponding Angles and
2. The Z or N angles as shown here
This should suffice.