A group of very small, very faraway islands in the Pacific Ocean
, starting about 1500 km south of Hawaii
and stretching roughly south-east towards Tahiti
Most of them -- Washington, Fanning, Kiritimati, Malden, Starbuck, Vostok, Flint, and Caroline Islands (naming them from north to south) -- form the easternmost part of the Republic of Kiribati.
Kiritimati and Fanning, at least, are inhabited, with several hundred people each. Kiritimati was formerly known as Christmas Island, of which it is the I-Kiribati version: it is pronounced Kirisimas. However, this is not the Christmas Island south of Indonesia and belonging to Australia. It may be that some of the others have also been renamed.
They are "easternmost" looking at a map, but the International Date Line passes through Kiribati, or used to: to cash in on the millennium they moved it so that all I-Kiribati territory was included in the new day. Caroline Island is at 150° W of Greenwich.
And just to be a bit more confusing, that's different from the Caroline Islands that make up the Federated States of Micronesia, also in the Pacific.