The physical layers hold the actual PC circuit traces in copper conductors. Physical layers are separated by thin layers of insulation called substrate or prepreg.
The design layers contain additional information for the construction of the board, specifically top and bottom silkscreens, top and bottom solder mask, top and bottom solder paste screens.
Just like photoshop when you compose an image it has several layers to it say foreground,background,subject etc.They all combine to form an image.
Similarly, we have layers in PCB which together make up the PCB.
They are:
1. Track layer(electrical connect)2. Silkscreen (words written)
3. Solder Mask (Covers the copper track to provide protection)
The tracks can be on top as well as bottom. Several sophisticated boards like Raspberry Pi has 4 layer boards too, where two layers are sandwiched between the visible ones.
As far as design software are concerned. The best for a hobbyists is Eagle and KiCAD.
Eagle is restricted in free version but has lots of support and libraries available.
KiCAD is no limits open source. But not very great support.