The Heroquest is a uniquely Gloranthan phenomenon, and comprises two forms- the Greater Heroquest and the Lesser Heroquest, on which more later (although note, this is my distinction, and not canonical).
Because the Gods are separated from the mortal world, they can interact only indirectly, but they still are the ‘fundamental truths’ by which the world operates. The Sun really is the Emperor Yelm, rising from the Underworld in his chariot, and traversing the Sky, before sinking down to travel back through the Underworld at night. The storms really are the breath of Orlanth, or Storm Bull, or another of the Air Pantheon, and so on.
At its basis, the Heroquest is a way of reaffirming their truth, by reenacting the myth behind them, and drawing that benefit on locality, Tribe, Clan, Kingdom or Empire. Reenacting the myth of Orlanth forming the Storm Tribe draws the Orlanthi people together, whilst going through the myth of Chalana Arroy, and how she healed the world might draw Her healing benefit onto some or all of the participants, their Tribe, Clan or Kingdom, and so on.
In a Lesser Heroquest, whilst the participant(s) enter(s) the Hero Plane, observers still see them stepping through the ritual in place, typically in a sanctified area, although they are acting the role of the Gods.
In a Greater Heroquest, the reenactment is on a far larger scale. In a Quest about travel, then travel occurs. In a Quest about gathering people, people are gathered in a non-pre-arranged fashion. This occurs partly within the Hero Plane, but simultaneously in the Physical World, or sometimes entirely within the Hero Plane. An observer may see the Quester vanish, or fall down, or mechanically act, with silvery glowing eyes. The effects of a Greater Heroquest are, unsurprisingly, greater, but the risks also higher, and potentially catastrophic. An example of a Greater Heroquest is Kallyr gaining the Star on her brow from a long dead Sky God (the myth is unknown). Lesser and Greater Heroquests (or Greater and Greater. Or very rarely Lesser and Lesser) can interact, for example, the Lunars attempted to extend the Glowline with a Lesser Heroquest to found a new Temple of the Reaching Moon in Sartar, but Kallyr and her companions infiltrated it, and performed their own Greater Heroquest, to draw back some of Orlanth’s companions, which resulted in the Dragon Rise. A rarer kind of Greater Heroquest is the quest to make a new Myth. This is the stuff of changing the world, and is the mark of a very great Hero of their Cult.
Commonly Known Examples of Heroquests are:
Chalana Arroy Heals the Scars
Elmal Guards the Stead
Ernalda Feeds the Tribe
Humakt the Champion
Issaries the Concilliator
Lhankor Mhy Finds the Truth
The Making of the Storm Tribe
Orlanth and Aroka
Flavour text for how these quests may work can be found in the game “King of Dragon Pass”, but local versions of the myth will vary, and the tale can change in the telling, so unlike a fairly linear computer game, these myths will not be pinned down so easily, with local events, such as ‘Bloofer Ladies’ changing what specific form of challenge the Hero faces!
A similar take (which may be shamelessly used) is to be found at this website, where he uses the term ‘Reenactment Heroquest’ and ‘Practice Run Heroquest’ largely in line with my ‘minor’.