This right simply means the right to travel outside Nigeria. Before a Nigerian will travel outside the country, it is mandatory that he/she posses a valid international passport issued by the government of Nigeria. The implication is that every Nigeria citizen has the right to own a passport.
However, you must meet up with certain requirement in order to be issued a passport and the requirement must not be so tough in order to disqualify or discriminate certain classes of people.
However, it is important that before you can travel out of Nigeria, you must have a valid visa of the country of your destination. Visas are issued by embassies of the country which you intend to visit. Without a visa, visa on arrival or other satisfactory means of lawful travel, Nigerian authority may be justified in refusing you exit from Nigeria at the airport or certified place of departure.