The Host came up with the idea to entertain the pilgrims on the way to and from the sacred place where St. Thomas a Becket was brutally murdered by Henry II's knights. The criteria includes that each pilgrim would tell two tales each--one on the way there and one on the way back. The tales will be judged by the Host on two criteria: entertainment value and moral lesson. The winner of the contest will enjoy a meal paid for by the remaining pilgrims at the Host's Taberd Inn.
The tales begin with the drawing of straws. The Knight's tale is told first since he is the highest ranking pilgrim, and from there the tales are told based on reaction to one another and who decided to jump in when.
It's thought up by the man who runs the Tabard Inn, in Southwark, where the pilgrims meet, who is usually referred to as the "Host". He talks to the pilgrims, about to set off for Canterbury, and proposes a game:
'...as ye goon by the weye
Ye shapen yow to talen and to pleye' (771-2)
The Host then stipulates the rules of a tale-telling contest (see GP 766-809). Each pilgrim has to tell two tales on the way to Canterbury, and two more on the way back. He himself will leave the inn and travel with them in order to judge the contest, and that, when they return to the tavern having been on their pilgrimage, the person he judges the winner will eat dinner (at his tavern) paid for by all of the other pilgrims. Who will the winner be?
That is to seyn, that telleth in this caas
Tales of best sentence and moost solaas
Sentence is moral sententiousness, moral instruction. Solaas is entertainment value, fun. These are two totally different criteria.
The Knight is selected by the drawing of lots ('the cut') - though this can be seen as a little suspicious, so keen is the Host on having the upper class characters to tell the stories. After the Knight finishes his tale, he immediately turns to the Monk, before the Miller buts in. So you well might be suspicious of the Knight being chosen.
The game isn't completed. No-one tells four tales, and the winner is never announced. In fact, in Fragment 10, (line 25) the game is stated as telling one tale each!