There's something like 6 one way valves that let your heart pump the blood out of your leg a little bit at a time. When they wear out, there's not enough pumping action at times to replace the blood as often as necessary. (also, the veins aren't rated for the pressure, which is why they blow out, and you get varicose or spider veins.)

But there are alternate paths for the blood to flow. If you mangle the larger deep veins, the blood will still circulate out secondary paths. And literally the next day, my foot was pink, and I wasn't winded climbing the stairs, and my legs weren't lead weights by the end of the day.