As a godparent of 4, I take the responsibility rather seriously.
The godparents are responsible for the spiritual upbringing of their godchildren. Of course, the parents still need to teach their own children, however, the godparent needs to reinforce that teaching, set a good and proper example, and make sure the child is being raised as a good and decent Orthodox Christian.
In the old country if anything happened to the birth parents, the godparents would take and raise the child.
Also note that godparents cannot marry. Therefore, as a single woman, I would not be allowed to marry the single man, who became the godfather to my godchild. (...this of course is if the child is getting a godfather and godmother.)