Underpricing is when a private firm transforms into a public firm and their shares have a price below the market value. Because of the expectations are unknown and they have to compensate the investors for the risk they are taking.

The first step to understand the meaning of underpricing is that when a firm does a Initial Public Offering the stock normally is under the market value, in order to make more attractive their stock. 

Nevertheless, a stock is not going to be below the market value all the time, because the laws of supply and demand will do that the stock reach a normal price.

An example of underpricing could be the next one:

In Spain, we have had recently the AENA´s IPO. The first day the prices were from 58€ per share, after two weeks, the value were from 84€ per share, so many investors took advantage of this underpricing.