Your muscles are still in a state of recovery after training for several hours. If you think of it like a small cut on your arm, it may help you visualize what is going on. If you cut yourself, blood (white blood cells, red blood cells, platelets) rushes to the area. This increases swelling in the area, however the goal with this to provide new material for your body to rebuild itself. Something very similar occurs after weight training (only to a lesser degree of injury), and the bigger your muscles become, the more your veins will increase in size to support the necessary increased blood supply.
I have a vein on my left shoulder leading to my upper chest that was not there even two years ago. What I mean is, it was obviously there, but it was never large enough to see as clearly as it is now. I am also bigger than I was years previous and using more weight which explains why my body compensated by increasing the size of a vein in that area. If you look at Ronnie Coleman's biceps, the huge vein running across looks as big as some people's wrists. That is because of the increased blood supply that his muscle needs.
Bottom line, for hours after lifting, your body is in a state of repair. That means increased blood flow to the area with your glycogen levels even contributing to how visible many of your blood channels are.