These commands tell the oxen to either step towards the other (put in) or away from him (put out). They are useful for creating space to get between them for hitching or other purposes, or for squaring them up in preparation for pulling or especially backing up. If their back ends are splayed out with respect to each other, they will diverge as they back up and progress will eventually halt. Put in/put out can also be used to sidestep the oxen to aim a cart when backing it into a barn.
When the oxen are pulling a heavy load and they turn, the chain will bear against the inside ox's leg, which is uncomfortable or can even cause injury. Put out can be used in conjunction with the turning commands to tell the ox to step away from the chain.