Taking responsibility means, as a representative of your company, you are ready to sincerely apologize to a customer on behalf of your business, even if the problem or situation that caused the customer's frustration was not your fault. Apologize and do your very best to ensure the issue gets fixed as quickly and smoothly as possible.
Remember that an apology is the key to showing a customer your deep commitment to their satisfaction. Apologies are important, but often times, "I'm sorry" is not enough. Just keep your words sincere and genuine. Your customer will appreciate your efforts to make the situation right.