The vertical line test is where you take a pencil or any vertical object and you move it across a function. If that vertical line intersects a graph more than once it would not be a function because for it to be a function it has to have one input value and one output value.
If you can draw any vertical line which intersects the graph more than once then the graph does not represent a function.
The intersection shows that for a given value of x in the domain there is more than one value of f(x). So this is a one-to-many relation and is not a function because a function must be one-to-one or many-to one.
