Omiyage are consumable souviniers. They are usually candy or crackers, but almost anything edible is able to be used as Omiyage. Meibutsu are famous products associated with a certain region. Each prefecture in Japan has diffent regional specialties. Yamanashi, the prefecture Ben and I live in are famous for their grapes.
Omiyage/Maibutsu are a huge part of Japanese culture. When someone travels, they are generally expected to bring something back for their work so that their coworkers can enjoy the experience as well. It seams to be a way of letting the people you work with know that you thought of them while you were gone. It is absolutely expected that Japanese people will provide Omiyage at work, but as a foriegner coming to Japan, it's not neccessarily expected of you. For those of you coming to Japan to start work, bringing omiyage will make a good impression on your coworkers.