What does Chaucer say that people long to do when spring comes?

Chaucer says that people want to go on pilgrimages in the spring. He begins The Canterbury Tales by describing a time "whan that Aprille with his shoures soote"—that is, when April with its soft showers of rain—"the droughte of March hath perced to the roote"—that is, the soft showers have destroyed the dry time in March, piercing it to the very root. He goes on to describe more specifically how this happens, saying how the showers "bathed every veyne in swich licóur / Of which vertú engendered is the flour"; so, the rain bathed the veins of the trees and plants with the kind of water that has the power to create flowers. He describes at length how the constellations are configured, and how the birds sing, at this season. He finally says, "Thanne longen folk to goon on pilgrimages;" that's what they want to do in the spring, to seek out strange lands to travel to. Specifically, they want to go to the shrine of Thomas Becket, the martyr who healed them when they were sick. Interestingly, all of this—the first 19 lines of the prologue—is written as one sentence.

The answer to this question can be found in the "General Prologue" to The Canterbury Tales. In the prologue, Chaucer says that, when April comes into full bloom "and smale foweles maken melodye," "so priken hem Nature in hir corages / Thanne longen folk to goon on pilgrimages." Chaucer is saying that when Nature comes into full bloom in spring, this stirs in people a desire to go on pilgrimages.
Spring inspires "palmeres for to seken straunge strondes"—"palmers" is a term generally used for those who were committed pilgrims; in Spring, according to Chaucer, they were inspired to seek strange lands. But most of all, according to the Prologue, people are inspired to travel to Canterbury, "the hooly blisful martir for to seke / That hem hath holpen whan that they were seeke." This "holy blissful martyr" who helped the sick is Thomas Becket, whose tomb was such a popular destination for pilgrims following his death during the reign of Henry II that the jewels were all stripped from his tomb by overzealous visitors.
https://www.poetryfoundation.org/poems/43926/the-canterbury-tales-general-prologue