We need to bring our passports when traveling from one country to another because it serves as a means to filter and control the movement of people across borders and it provides us with an internationally recognized document to identify us.

A passport is a travel document. It is issued by the government that a person is a citizen of as proof of the person's identity and nationality. Requiring foreigners passing into a country's borders to show their passports allows a country to identify who is entering and who is going out. This serves as a means of policing, so that countries can keep undesirable people out. These includes terrorists, criminals, and individuals from countries that the receiving country has not allowed to enter. It is also a way to keep individuals restricted from travel from leaving his or her home country.

Your passport also serves as a proof of your nationality. If you should ever need the assistance or services of your home country while in a foreign land, your passport is the proof that could identify you as a citizen of your country. 

Finally, your passport is also the only proof of identification that hotels and other establishments will accept from foreigners. When you check into a hotel or go into an establishment that requires its customers to present an ID, your passport is often the only form of identification that will be accepted abroad. So, without it, you might not be able to check in at your hotel, transact at a bank, or receive services. 

That's why we all need to carry our passport when we travel. Otherwise, we won't be able to enjoy our travels because we might be denied services or our home country might not recognize us. And of course, carrying a passport is a way of helping governments police their borders.

Source:

Passport: https://en.wikipedia.org/wiki/Passport