Whenever one hears a Beracha, he must answer "Amen" to the Beracha especially after one hears a Beracha for the purpose of fulfilling his obligation to recite it, for example, if two people want to drink water, and one recites the Beracha on behalf of them both. The one who listens to the Beracha should answer "Amen." However, if, for whatever reason, he did not answer "Amen," he has nevertheless fulfilled his obligation. As long as they both had in mind that the listener should fulfill his obligation through listening, he fulfills his requirement, even though he did not answer "Amen."
Interestingly, the Poskim draw an important distinction between one who answers "Amen" to a Beracha he hears to fulfill his obligation, and one who does not answer "Amen." If one does not answer "Amen," he fulfills his obligation, but he is not considered to have actually recited the text. By contrast, once a person answers "Amen" to a Beracha to which he had listened with the intention of fulfilling his obligation, he is considered to have personally recited the Beracha. He is not only credited with having recited a Beracha, but is regarded as having actually recited the words with his mouth.
The practical difference between the two cases, as Hacham Ovadia Yosef explains, relates to the possibility of changing ones mind after fulfilling his obligation by listening to a Beracha. If one answered "Amen," then he is considered to have actually recited the Beracha, and so he does not have the option of changing his mind and not eating or drinking. If he does not eat or drink after reciting "Amen," then he is in violation of reciting a Beracha in vain, even though he did not actually recite the words of the Beracha with his mouth. But if he did not answer "Amen," then he is not considered to have personally recited the Beracha, and so although he has fulfilled his requirement if he still wishes to eat or drink, he has the option of changing his mind.
Summary: One should answer "Amen" after listening to a Beracha. If one listens to a Beracha with the intention of fulfilling his obligation to recite that Beracha, then after he answers "Amen" he is considered to have actually recited the Beracha, and therefore he must eat the food or drink the beverage, as otherwise, he will be considered to have recited a Beracha in vain. If, for whatever reason, he did not answer "Amen," he has nevertheless fulfilled his obligation and may eat the food or drink the beverage, but he is not considered to have actually recited the Beracha, and so he has the option to change his mind and not eat or drink.
