Obi age is a cloth to secure the shape of the tied knot of obi.
However, nowadays obimakura plays that role except some occasions, so obiage is positioned as a decorating cloth to cover the obimakura and adjust the top of the obi. Hanhaba obi which doesn’t need obimakura, doesn’t also need obiage, but sometimes you use it as a decoration.
There are tricks for tying them elagantly, and it might be hard if you’re not used to it. One way to do it is not to make a knot, just adjust the shape and insert it between the obi and datejime.
Obiage for winter and summer are distinguished, and there are differences in ranks. Basically, translucent materials are for summer, and otherwise for winter.
Material mainly used are shibori, rinzu, and chirimen. For furisode, obiage with soshibori (elagant patterns on the whole cloth) is normally used, not only because it needs to have high quality, but also because the obiage needs to have volume in order to match with kimono and the obi. For formal kimonos, white obiage with golden strings is the basic, and rinzu or shibori is used.
When wearing casual kimonos, some people enjoy by using rectangular scarves, or items made by cutting cloths.