Often, the second nameserver also kicks in not just if the server goes down, but if traffic gets high and it's busy (load balancing). Sometimes they are in different locations as well, so that a catastrophe won't take both out at the same time. One may be in a datacenter on the east coast and another on the west coast.
BTW, most people usually configure their routers to use the DNS severs of their ISP since it's the fewest hops. Sometimes you can set your own computer/router to use your own DNS servers instead (usually temporarily), which can take some time out of the propagation process when DNS changes are made or started.