The y-intercept is where a line crosses the y-axis, which is when x = 0.

Parallel lines on a graph mean that two or more lines have the exact same slope as one another (which is what makes them parallel: they cannot touch, and if their slopes differ, they eventually will sooner or later). The y-intercept is a tool to see just how close or how far each line is to one another:

y = 3x + 5

y = 3x + 4

y = 3x + 6,783,648,213,464,987,123

Each of these lines are parallel: they each have the exact same slope, so no matter what value up put into x, they will never touch one another.

When we put 0 into the value of x, we see where they cross the y-axis--find the y-intercept:

y = 3 * 0 + 5

y = 0 + 5

y = 3 * 0 + 4

y = 0 + 4

y = 3 * 0 + 6,783,648,213,464,987,123

y = 0 + 6,783,648,213,464,987,123

The y-intercept, thus, is a tool to help define a point on the line to determine where on the graph it resides.