The pilgrims are going to Canterbury to worship St. Thomas a Beckett (well, that's what they say, but it's also a trip for leisure and fun). They began at a tavern called Tabard Inn in Southwerk and probably left on April 17th. Originally, Chaucer's plan was to have each person tell two tales on the way to Canterbury and two tales on the way back, which would equal 120 tales. However, he only completed 24 tales (understandably!).
They were on a pilgrimage. A pilgrimage is a physical journey to a holy place. It is supposed to be a spiritual event. In the prologue, Chaucer's narrative persona says:
The hooly blisful martir for to seke,
That hem hath holpen whan that they were seeke.
(They go to seek the holy blissful martyr who will help them when they were sick.)