Thanks guys!
The ping works in both directions on Debian, but I still cannot access the Internet from the Galileo. I tried to make my PC as a router with the command:
sysctl net.ipv4.ip_forward=1
and I also added a default route on the Galileo to my PC (just like Jacker.Wang says), but it doesn't change anything. Is there a better way to access Internet from the Galileo through the PC?