What does this scale mean?

$$\log_{10}~\mathrm{pg}/\mathrm{ml}$$

I do not understand the scale. How do I convert this to a standard concentration (without the logs)?

To expand upon the comments, the y axis in this graph is simply the log of the concentration in pg/ml. To convert you use the equation $$C = 10^{y}$$ where y is the y value and C is the concentration. Note that in older literature, log was oftentimes assumed to be base e whereas nowadays we assume base 10. The figure (thankfully) clarifies this potential discrepancy.