Where are the pilgrims going in "The Prologue" from The Canterbury Tales?
The initial 30 pilgrims are all gathered at the Tabard inn prior to starting their pilgrimage. The end goal of their travels is Canterbury, which seems like a cop out answer. The reason that all of the travelers are going to Canterbury is to pay their respects to Saint Thomas a Becket, the Archbishop of Canterbury. In the year 1170 Becket was killed by the order of King Henry II. Becket was killed because Henry was angry that Becket sided with the church more often than he sided with the king (that's the general gist of it anyway). Becket went down in history as a martyr and a saint for standing up for his faith, and the 30 travelers are on a pilgrimage to see the tomb of Becket.
Ready to start upon my pilgrimage
To Canterbury, full of devout courage,
There came at nightfall to that hostelry
Some nine and twenty in a company
The pilgrims are on a pilgrimage: this is a journey to a holy place. During medieval times (Chaucer's time) people often would visit shrines or even the Holy Lands for the good of their souls. All the people listed in the Prologue are going to Canterbury Cathedral. This is considered a holy place because Thomas a Becket, the Archbishop of Canterbury, was killed by King Henry II's men, and became a martyr and saint.
As the pilgrims travel they agree that when they stop for the night at an inn, each will tell a story as a means to entertain the others. Chaucer includes himself among the number of pilgrims, and gives a running commentary as to who is a truly good person, and who is putting on a show for the others.