Onbu is the way to carry a child papoose style (in other words piggyback). It is customary in Japan to carry a baby tied onto its mother's back using a long sash. The baby faces the mother's back with its legs spread and its hands on her shoulders. Supposedly this gives the child a feeling of security and an attitude of dependency. Whether that is true or not, I don't know, but it is a means of both holding your child and keeping your hands free to do other things.
In the picture Ranma is holding Happosai in this manner after a botched magic potion left Happosai mentally a baby (anyone else wonder why it is Ranma that appears to take care of babyfied Happosai instead of one of the girls, since in Japan taking care of a baby would be a task for women).
Getting a baby into those slings unassisted can be troublesome though. Here is a Youtube video of someone putting their baby in one type of them without someone to help them. http://www.youtube.com/watch?v=6Gmw-sZByTA