The "purple Host" of the poem is a symbol of whoever has met with success today; it could be a conquering army, as seems literal, or it could be any person or group that has triumphed, figuratively. The references to purple and host are both associated with the divine, and so perhaps Dickinson implies that whoever has meets with success enjoys something that feels like divine favor. However, she claims that the successful actually understand success or victory the least. Those who are victorious cannot properly define success, because they do not understand its opposite. Those who feel the "sorest need" of success—those who lose or lack it—understand victory better than those who achieve it because they know how it feels not to.
In "Success is counted sweetest," Dickinson writes:
Not one of all the purple Host
Who took the Flag today
Can tell the definition
So clear of victory
In this context, "purple Host" refers to a conquering army, which, having defeated its enemy, captures its flag in victory.
In the ancient world, particularly during the era of the Roman Republic, purple was the color both of royalty and of victory. Victorious generals would wear the toga picta, a solid purple toga decorated with gold, as a symbol of their success in battle.
Dickinson is drawing a contrast between those who know success and those who know failure, and making a statement about which of the two would appreciate success more. Dickinson makes her point by using the image of a victorious army in contrast with a dying, fallen soldier. She is inferring through this image that only the dying soldier fully understands and appreciates victory. In the same way, she is saying that only those who have known failure can fully appreciate success.