Food that was poured from a kli rishon onto another food will cook a kelipa of the food it touches. A kelipa is the smallest outer layer of the food that can be removed in one shot (ש”ך יו”ד צו ס”ק כא). For example, if you pour non-kosher soup onto a kosher piece of meat, the outer layer of meat becomes forbidden.
If the stream was poured steadily from the pot without breaking up in the air, we treat the kelipa as if it was cooked on the fire in a kli rishon (ש”ך יו”ד קה ס”ק ה). For example, if one poured milk from a kli rishon onto a piece of meat, the outside layer of meat is forbidden, and all the milk is forbidden. The reason that all the milk becomes forbidden is because every drop of milk touched the meat as it was poured and therefore a kelipa of every drop becomes forbidden, which is technically all the milk.
If the stream broke before the first drop of liquid touched food, then the liquid does not have the power to cook like a kli rishon. However, rabbinically, there is still a transfer of taste, and therefore a forbidden food which was poured onto permitted food can make the permitted food rabbinically prohibited even if the stream broke.