The past — but a particular flavour of past: the days of long ago, remembered fondly. It is a noun, though you will most often meet it doing an adjective's job in the phrase 'of yesteryear': the stars of yesteryear, the trains of yesteryear, a Taipei of yesteryear. That is the shape to learn, because the bare noun on its own ('yesteryear was better') sounds odd to modern ears. Two things govern how it feels. First, it is warm: it does not just mean 'earlier', it means earlier and gone and missed — you would not write 'the wars of yesteryear', because the word carries affection. Second, it is literary and a little old-fashioned itself, which is part of the joke when journalists reach for it in headlines about old cars, old films and old sweets. In ordinary speech people say 'the old days', 'back in the day', or 'years ago'. The word is not old folk speech, oddly enough; Dante Gabriel Rossetti seems to have made it in 1870 to translate a French line about the snows of last year — 'où sont les neiges d'antan' — and it kept the sad, backward-looking colour of that line ever since. Note also that despite the definition line above, the word is a noun, not really an adjective; 'existing in the past' is what the phrase 'of yesteryear' does, not what the bare word is.