Everything started in the 22nd century, when Doraemon (a faulty robot) was auctioned to a family suffering from abject poverty. This family, the posterity of Nobi Nobita, suffered dramatically all thanks to the debts which Nobi Nobita left behind to them as his legacy. Nobita's great great great grandson (correct me if I am wrong) decided that there wasn't a way out of this mess, and hence decided to send Doraemon back in time, to 250 years ago, to where Nobi Nobita lived, to help Nobita become a better person. This would ultimately change the future and improve the living conditions of Nobita's descendants.
Doraemon arrived in the year 1969, on the Japanese New Year. He popped out of Nobita's desk drawer, and from then on lived with Nobita, his mission was to prevent Nobita from becoming a failure. Each time Nobita was suffering from some kind of trouble, Doraemon would dig into his fourth dimensional pocket and use his myriad of gadgets to rectify the problem
It seems Doraemon has succeeded, because during time travels to the future, Nobita saw himself married to Shizuka and not Gian's ugly sister. He also witnessed his descendants living in much better conditions than before and Nobita's great great great grandson had recovered from bankruptcy (because future has changed, they have never been in bankruptcy) and was able to afford a superior robotic cat, Dorami, as their household robot.
During the series, both on TV and manga, Doraemon and Nobita tell a story of a duo who are destined to change each other's life, and how as long as we have hope, there's still a way out of a dead-end. If we are determined, two wrings can make one right. I strongly recommend to those who haven't watched Doraemon to do so, as Doraemon (the name of the series) is not only a strong portrait of Japanese lifestyle and their idiosyncrasies, but also a cartoon which manifests how bravery and trust are superior qualities and their application will only benefit us in life.