Vertical line test tells us whether the graph represents a function or not. This test states that "if a vertical line intersects the graph at only one point then it is a function otherwise not" Now, if any vertical line intersects the graph at two points then it means that for a value of x, we have to y values. In other words the x value has not unique y values which doesn't satisfy the condition of a relation to be a function.
Therefore, if the vertical line intersects the graph at only point then only each x values has a unique y values.