The te form of a verb, followed by the verb iku or ikimasu ("go"), expresses an action that moves away from the location of the speaker, or moves into the future. Here iku or ikimasu is used as an auxiliary and by convention is written in hiragana rather than kanji.
Kare wa kyū ni heya o dete itta.
He left the room suddenly.
「Viewpoint: The speaker is or was in the room when the person left, thus the direction of their leaving is or was away from the speaker.」
Mainen, Janetto-san wa kurisumasu ni kuni e kaette ikimasu.
Every year Janet returns to her (home) country for Christmas.
「Viewpoint: The speaker no doubt remains in the country from which Janet leaves, and that country is probably their home country.」
Kono machi no jinkō wa dandan fuete iku.
This city's population will gradually increase.
Hope this helps!
°˖ ✧◝(○ ヮ ○)◜✧˖ °こゆうきあいはら°˖ ✧◝(○ ヮ ○)◜✧˖ °