Its exactly like a histogram
Symmetric boxplot: the median is generally in the middle of the box. So, if you measure either side of the median, they should be approximately the same in length. However, a simple observation can determine this - look at the boxplot and ask yourself: are both sides (divided by the median) equal?
If the answer is yes, it is symmetric
If the answer is no, it is skewed
It can be
Positively skewed: the median will be closer to the left end of the boxplot. The right end will be longer - 'gradually tailing off of data values to the right'
Negatively skewed: exact opposite of positively skewed
The median will be closer to the right end of the box plot, and the left whisker will be longer, tailing off in the left direction
I really hope that makes sense....