Фуфайка refers to a padded or quilted jacket, often associated with working-class attire in Russia. It's a distinctly Russian garment, not a common word you'd find in many songs.
In the song, it's used to evoke a sense of warmth, comfort, and a down-to-earth, authentic Russian spirit, as in "Русский Ванька тёплая фуфайка" (Russian Vanka is a warm padded jacket). This word paints a vivid picture of a particular cultural identity.
"Русский Ванька (Russkii Van’ka)" is a really fun, spirited song that's all about a deep, almost defiant love for Russia and a simple, self-sufficient way of life. The singer, who calls himself "Русский Ванька [Russian Vanka]," describes his "сердце балалайка [heart a balalaika]" and his "тёплая фуфайка [warm quilted jacket]" as symbols of his Russian soul. He makes it clear that he doesn't need anything from anyone else, saying "Мне ни от кого не надо ни шиша [I don't need a damn thing from anyone]."
The lyrics are full of humorous and blunt declarations. He says, "У России нету края Ведь она в моей груди [Russia has no end Because it's in my chest]" and believes that "Из России уезжают Только те кто не любил [Only those who didn't love leave Russia]." He even pokes fun at Western culture, stating he "не плакал без хот-дога Проживу без USA [didn't cry without a hot dog I'll live without the USA]" and that "Там не хватит по любому Места для души моей [There won't be enough Room for my soul there]. He finds contentment in simple things, like not throwing away "пакеты И дырявенький носок [bags And a holey sock]" and being perfectly fine "без ЕС и гей-парадов [without the EU and gay parades]. It's a song that celebrates a very specific, proud, and independent Russian identity.