I assume that you know that parallel lines are lines that never intersect. Slope is a mathematical way to talk about the steepness or the direction of a line, so that is why this topic is coming up now. Now draw any other line whose slope is 2. You should see that these lines look parallel. What's more, if you draw any other line parallel to these and then compute its slope from your graph paper, you will see that it will also have slope 2.
Parallel lines have the same slope.
Perpendicular lines are a little more complicated. You know that perpendicular lines intersect at a 90 degree angle. If you were walking along one of the lines you would have to make a right turn or a left turn in order to move along a perpendicular line. This change in direction means that the two lines have different slopes. But the fact that you always make a 90 degree turn means that their slopes are related.