Translation:До побачення, друзі!
"ї" palatalises the preceding consonant (if it is possible), "и" does not. In case you are not familiar with the phenomenon, it means that the middle part of the tongue is raised while pronouncing the consonant.
The difference in vowel quality is a bit similar to the difference between bit and beat. The Ukranian и is a vowel that has your tongue a little more to the back and a little lower. The Ukranian і is a usual tense and clear [i] sound, like in meat, heed, see, me, leave.
Since neither of is a native speaker, we should just memorize which of the sounds a certain word has. :)