They aren't the only ones, actually. St. Nicholas Day is big in continental Europe, St. George Day on the Balkans, St. John in Northern Europe and the Baltics (although based on pagan summer solstice festivities).

In the calendars of the various Christian churches that venerate saints, there is a handful of saints for every single day of the year (except maybe the leap day) and they will be remembered during the mass.

Now, how do some saints become more important than others?

Whenever a new church in a city or town of village is built, it will be consecrated to a saint and that saint's day will be celebrated in a little more special way than the others. The reason why one saint will be chosen over another are manifold. Sometimes the sponsor of that church, in the middle ages that might have been a local noble, had a favourite saint; or the town had come into possession of certain relics; or the place is associated with a saint's life or death.

Anyway, when the local church celebrates its patron saint, that's a holiday and occasion to feast. As for saints like Valentine, due to the legends and stories that are associated with them, people sometimes invent a special custom (and not just a more hearty dinner than usual) to fit to the saint. St. Nicholas helped young maidens by gifting them gold -- today we give gifts on his feast day, December 6th. He becomes Santa Claus in America. Valentine brought couples together, so we celebrate it as a lovers' day.

Over time, some cities become more important, and thus their patron saint too. In some instances, a church and its relics gain a reputation that miracles happen there more often than elsewhere, so they attract many pilgrims and and inspire the consecration of more churches to that saint in other places. Some saints are just fundamental figures of Christianity and venerated pretty much everywhere, like Mary or John the Baptist. Or they were popular even early on the Roman Empire, like George or Nicholas.

As for Patrick, all of Ireland has him as favourite saint because he propagated Christianity in Ireland. So when many Irish people came to America, they brought the celebration of St. Patrick with them. Outside of Ireland and the places associated with Irish emigration, St. Patrick's Day is not really a big thing.