That means that there is something on the bottom that shouldn't be there. Look for a small trace segment on the bottom that is overlapped by another trace. It might even be on the part (and should be edited to correct). An overlap error means that one signal has crossed over another signal on the same layer. It generally is a bad thing and should be corrected. In this case, you could probably live with this error, but it is bad practice to not correct these type of DRC errors.
It could arise when you rout into a pin with a signal, then rout out of a pin with the same signal. If one of these branches does NOT hit the pin, then another signal is created. It's usually best to rout FROM a pin to a trace segment, since the pin may NOT be on the grid, but the end of the trace segment will be. In your first picture, there is an airwire that might indicate this condition.
Re: What is this shaded thing on the PAD ( Eagle PCB)
I think you just go to DRC and then click "clear errors" and that gets rid of it....then if you want it back then just run another design rule check..(DRC).
DRC is where you tell the program what not to like....eg holes less than 1mm away from pcb edge...vias less than 1mm diameter..etc etc