In "A Christmas Carol", why does the Ghost of Christmas Past hold a branch of fresh green holly in its hand? What does it represent?

The three ghosts that Scrooge encounters not only tell him things they wish him to know, but also reveal symbolic insights through the descriptions Dickens uses to present them. For example, The Ghost of Christmas Present takes Scrooge to the marketplace and encourages him to see all the abundance around him: 

"There were pears and apples, clustered high in blooming pyramids; there were bunches of grapes, made, in the shopkeepers’ benevolence to dangle from conspicuous hooks,...

The three ghosts that Scrooge encounters not only tell him things they wish him to know, but also reveal symbolic insights through the descriptions Dickens uses to present them. For example, The Ghost of Christmas Present takes Scrooge to the marketplace and encourages him to see all the abundance around him: 

"There were pears and apples, clustered high in blooming pyramids; there were bunches of grapes, made, in the shopkeepers’ benevolence to dangle from conspicuous hooks, … there were piles of filberts, mossy and brown..."

This is a way of reminding Scrooge to appreciate his blessings and daily life, and despite rejecting the notion at the time, he later takes this advice to heart when he urges the boy in the street to go to the market and purchase a large goose for the Cratchit family.

The Ghost of Christmas Past is presented as an odd hybrid of old man and child, whose form appears to shift with the light and shadows as it moves. But the mode of dress in interesting:

"It wore a tunic of the purest white, and round its waist was bound a beautiful, shining belt. It held a branch of fresh green holly in its hand; but had its dress trimmed with summer flowers. But the strangest thing about it was, that from the crown of its head there sprung a bright clear jet of light..." 

The presence of both green holly, an evergreen plant that produces red berries in winter, and summer flowers, which bloom for a shot period of time warm weather, shows that this ghost is a reminder of the cycles of life and of time passing. Scrooge rarely thinks of his past and the ghost shows him memories that are both pleasant and sad. He grows emotional when confronted with the joys of his youth. The evergreen nature of holly is a way of suggesting that the thoughts of the past can keep us young even in old age, much as the ghost looks like both an old man and a child, and allows Scrooge in his old age to feel like a child again.

Since ancient times, the plant has been associated with fertility, but also with protection; this is one reason many people plant a holy bush close to their homes. The boughs are cut in winter to decorate the indoors with greenery, as a reminder that spring will come again; this tradition lent itself to the common depiction of holly on Christmas greeting cards since Victorian times into the present day, and its mention in many traditional Christmas carols such as "The Holly and the Ivy" or "Deck the Halls." The plant is thus also a reminder for Scrooge to embrace the magic and beauty of the Christmas holidays as so many  others around him do; even the Cratchit family, who have so little money, find ways to make the holiday special. Scrooge finally finds the joy and beauty in Christmas, and it renews his spirit, a renewal as powerful as the energy that keeps evergreen plants vibrant all year long.