Kiribati is associated with the first inhabited places to enter each New Year because parts of the country use the UTC+14 time zone.
Kiribati is an island country spread across the central Pacific Ocean. Its Line Islands, including Kiritimati, use Line Islands Time, which is UTC+14. That offset places those islands among the earliest inhabited locations to reach midnight on a new calendar date and therefore among the first to celebrate New Year's Eve's transition.
The situation became especially notable after Kiribati moved the International Date Line eastward around its territory in 1994–1995, bringing its widely separated islands into the same calendar day. The phrase “first in the world” can be imprecise because it depends on whether one means first inhabited land, first population center, or first official celebration. UTC+14 is the key factual distinction, not the country's capital.