The main objective of a passport is to verify the bearer's identity. The format is universal, so it is easy for immigration officials all over the world to find the bearer's name, address and nationality. Because the process for obtaining a travel document requires a government endorsement for each person who obtains a passport, this document is recognized universally.
The passport aims to tell immigration officials your nationality. The outside cover of your passport accomplishes this function because it bears your country's name. The inside page -- upon which your photo and personal details are stored -- states your place of birth and your nationality explicitly.
A modern objective of the passport is to facilitate safe travel all over the world. Passports identify for the host government individuals who are leaving or entering a country. When foreign nationals register at the local overseas mission or embassy while abroad, the traveler's home government can identify and help the traveler in an emergency.