How exactly does removing labor​ market rigidities reduce structural unemployment and increase potential output in an economy? Here I want to focus primarily on the potential benefits of labor market reforms such as a reduction in job security and trade union power and not their controversies. I wish to learn a few thoroughly explored reasons for how labor market reforms may decrease structural unemployment and increase the productive potential of the economy through improvement in efficiency.
Potential benefits of labor market reforms such as a reduction in job security and trade union power:

To find the answer to a reduction in job security, just apply it to your personal life(assuming you are employed). If labor market reform comes in and puts my job at risk, I would become more competitive and work harder in order to keep my job. This reaction would apply to most people. 

As for a reduction in union power, this is more macro scale oriented. What unions don't realize is that financially they are hurting themselves &amp; their company, albeit ethically/morally/quality of life at work they are gaining. So to keep things short and not go too far into controversial topics regarding unions, if union power is reduced, then market efficiency would increase from a financial standpoint not only for the firm, but for the macro economy and thus the employees. 

As for structural unemployment, if there are market reforms structural unemployment will almost always rise in the beginning, but usually fall back down and most times dip even lower than previous levels due to efficiency gains from adapting to the reforms. 

Hope this helps, I know it's not as detailed as you probably want it to be, but for that level of detail one must get into the controversial topics and pick a bias.