According to Clifford Bachman, "in the mid-ninth century Christians discovered in Santiago what they believed to be the body of St. James", the apostle. This quickly became a popular pilgrimage site. Santiago is Spanish or Latin for Saint James and Compostella is Latin based meaning 'field of stars'. Interestingly, it appears to be what the Spanish call the Milky Way.
There were several rallying points for pilgrims undertaking the walk. Some of the more popular ones were Vezelay and Le Puy, where there were famous cathedrals. The path takes you near Roncesvalles, where Roland died, and past many sites that were pagan shrines before they were Christianized. According to the entry on Wikipedia, Santiago was supposed to be the place where the souls of the dead gathered to follow the sun across the sea in Celtic legend.
From St. Jean Pied de Port it is 780 km to Santiago, so it is not a vacation for the faint of heart. People undertook the walk as penance for their sins. The walk has become popular again as people want to do something different for vacation besides lounge around at a beach and to prove that you did walk the whole length, people brought back local items that they could only have gotten in Santiago or in towns along the way. This is the origins of the souvenir. These days, you can buy a passport and get stamped along the way.
This website, has all the routes mapped out with photographs submitted by people who have walked the entire distance. It has tips and more to get you excited or interested about doing something different like this. I hope to do the pilgrimage myself someday.