Leap day exists for astronomical reasons, but changes in routines and astronomical anomalies have always tickled people's imagination. The history of leap year is well known and it goes back over 2000 years to the Roman Empire, to the reign of Julius Caesar. The leap year traditions we know about are not quite as old though.
In the past leap year was seen as a time when the natural order of things was overthrown and weird things could happen. Considering the natural order back in the day meant the men were in control, it's understandable why leap year then would become somehow linked to women. I say somehow linked to women, because here is where northern and southern and Europe take slightly different paths.
In the northern parts of Europe it became a tradition that once in four years, on leap day, a woman could propose to a man, instead of waiting to be proposed to. Since the day was already out of whack, women proposing to men for once didn't seem such an outrageous idea, right? And should the gent dare to refuse the proposal, he would have to buy her a gown (England), the fabric for one (Finland), or gloves to hide her bare ring finger (Denmark). Except if he was already engaged to someone else, of course. In that case she should have just picked her target more carefully!
In southern and eastern Europe instead, leap year is considered generally an unlucky period. In Greece getting married during leap year is considered bad luck, and in Italy a whole bunch of sayings highlight the unpredictable nature of this time: anno bisesto tutte le cose van di traverso (in leap year all the things go awry) or anno bisesto tutte le donne senza sesto (in leap year women become erratic). Maybe the inventor of the last one had met an erratic northern woman who had had the guts to propose to him! Who knows.
There are still women who prefer for the man to pop the question. It's considered romantic and it's traditional. Nothing wrong with that. Fortunately these days women who do feel like proposing to their partners don't have to wait for four years to do so. We can just go after the things we want in life, 366 days of the year. Even if leap day traditions remind of us of women's limited freedom in the past, maybe it should now be a celebration of how far we have come.