Before the Gregorian calendar we go by today we had the Julian calendar, which meant that the winter solstice (longest night) ended up on what we consider is the 13th of December. Just like midsummer was there supernatural beings out and about during this night, the Lussi night. For example was an evil man (Lussegubben) or woman (Lussi) roaming around but this has no connection, despite the name, to Lucia which came later. It is claimed that the tradition with a female light bringer might come from a pagan light goddess.
At 13th century the legend of Lucia became known here, by 14th century it was the name of 13th December, probably due to the close name of Lussi night. It was the longest night and Lucia (which comes from the Latin word of light, lux) comes and brings light to us. During the middle age, on the 13th you also slaughtered the pig and most of the Christmas preparations needed to be done. Nowadays the day isn't connected to slaughter but with saffron buns, ginger cookies and mulled wine.
Today the tradition with a light bringer is still active on many levels in our society. The main activity for a Lucia is to sing Lucia and Christmas songs. Sadly though, it's either a popularity contest (schools) or a beauty contest (cities). Kids get to do a Lucia procession ("Luciatåg") in school, usually one class is picked out and they "lussar" for all the others.
Cities and towns usually have a Lucia which the population can vote for, usually by seeing their pictures in the local newspaper. Gothenburg have this year focused on the singing so you haven't seen the girls, just been able to hear them sing and vote after that. Hopefully that will spread to more places. The national Lucia; "Sveriges Lucia" was more known before, I've barely known who had gotten the title since I was young and it was on TV, so unfortunately I can't say much about this.
A Lucia procession includes: one Lucia with a light crown, white gown and a red sash (which is symbol of Lucia's death), a "tärna" with (glitter) crown, white gown and a light in the hand and a "stjärngosse" with a cone on the head, white gown and either a light or stick with a star in the hand. In some processions, mostly for kids, there are also several Santa and ginger cookies.
To get it more visually what we do look at this info video:
Sources: Wikipedia, myself and Aftonbladet.