The gradient 4 means that the vertical coordinates on the graph rise 4 times faster than the horizontal ones. This is another way of saying algebraically y=4x. When x is 1 y is 4; when x is 3 is 12, and so on.
This is a straight line passing through the origin (0,0). If you draw lines parallel to this, all the lines will have the same gradient but are displaced from the origin. The intersect of the line and the vertical y axis is called the y intercept and this is represented by the constant b in y=4x+b and b can be positive or negative, negative values being where the line intersects the y axis below the origin (parallel lines to the right of the original line y=4x). Positive values of b are when the parallel lines are to the left of the original line.