In a box and whisker plot, the plot extends from the lowest to the highest values - the horizontal line goes from minimum to maximum. Remember that the range of data is simply the maximum less the minimum.
The three vertical lines (the two that compose the ends of the "box" and the one inside the box) represent the 25th, 50th, and 75th percentile (reading from left to right). The 25th percentile, for example, divides the data into two pieces - to the left of the line is 25% of the data, to the right of the line is the other 75%.
Now, remember that the median value in a set of data is always the number that divides the data into two equal sets, i.e., 50% of the data is below the median, 50% of the median is above the data. So, really, the median is the same as the 50th percentile, which is the vertical line inside the box.
Hope this helps!