It says the following:

• The vast majority of your data points in each sample have values close to zero, as indicated by the fact that both the median bars and upper/lower quartile perimeters are scrunched up at the zero mark
• There are many outliers in your samples, as indicated by the points outside the upper-quartile perimeter.

It does not look like you are plotting logged values. This looks like FPKM-normalised counts, or normalised counts on the negative binomial distribution.

Not that you can re-generate this without the outliers by specifying outline=FALSE to the boxplot function.

Kevin