Just saying half interest is a little vague as to whether it's referring to semen interest or possession. The others are right about the semen interest - some breeders will say they're retaining some percentage of semen interest in every bull they sell. Almost all of the time it will end up meaning nothing to the buyers because the seller never exercises that interest. Occasionally in the case of one that is shown, or turns out to be an exceptional sire they may want some semen for their use or may want to sell some - it shouldn't cost you anything unless you both choose to promote the bull and could make you some money. It's a little off putting to me when a seller states they're retaining a semen interest in every bull they sell, but like I said, it usually never happens, and I agree it's probably mostly a sales gimmick.
Half possession can be a viable alternative for two (or more) breeders to pool their money and be able to purchase a better bull than each could afford on their own, or for the breeder of the bull to retain an option to use him naturally. It's probably a lot more common with producers of registered and/or show type cattle than with commercial breeders. Maybe one breeder will use the bull for fall calving and the other for spring, or they split their possession a year at a time. If you think it sounds crazy then it's probably not for you, but I have owned partial possession of several different bulls over the years. Some turned out to make us good money, some turned out to be expensive cow fresheners - just like if I owned 100% of them, but with a little less monetary risk. It can be a good deal if you know and trust your partners.