Copper & plating density

The DFM tab shows the copper and plating distribution on the layers. It also shows unconnected copper that is not covered with a solder mask. To understand the plating distribution it is important to know that the board starts out with a (typically) 18 microns thick copper layer. During the plating process (when the plated holes and vias get plated), the copper layer’s thickness grows to about 60 microns. However, if the copper is unevenly distributed, the plating process will be uneven and some parts may get plated too much whereas other parts will not be plated enough. Over-plating may result in reduced hole diameters, under-plating may affect the quality of plated holes. Furthermore, uneven copper distribution may cause bending of the board at high temperatures. Panels built with different boards are often subject to uneven plating distribution. Once you know the plating distribution, you can improve it by adding or removing copper, or by rearranging the boards in a panel. Copper pours are a powerful tool to improve the copper distribution.

 
My board suffers from serious copper plating unevenness, better fix it.

Conclusion

The PCB Checker is a powerful tool for finding potential board manufacturing and quality issues that may go unnoticed otherwise. Where the DRC tab should not show anything because you ran the proper DR and ER checks in your board design tool and made sure that everything was all right before uploading the files anyway, the DFM tab is very instructive since not many CAD packages will do copper distribution graphs.

Even though Eurocircuits allows you to order a board with hoisted red flags, my advice is to correct if possible every issue signaled by the PCB Checker, critical or not, before moving into manufacturing.