Lady Galadriel's gift to Sam Gamgee was a small wooden box that contained a seed and some soil from Galadriel's own orchard in Lothlorien.
When Galadriel gives Sam the box, she says "For you little gardener and lover of trees, I have only a small gift."
She hands him a small box marked with a G. She tells him that the G may stand for Galadriel or Garden. She then tells him it contains dirt that is blessed with whatever power still remains inside her while she resides in Middle Earth. She tells him that the dirt will make any garden grow beautiful.
There is something odd to note, here. Sam does not open the box at this point and it appears that he does not open the box until he returns to The Shire to find a desiccated industrialized wasteland.
Once he does open the box, he finds that not only is there the dirt, but a seed as well.
The dirt and the seed are used to undo some of the effects of the damage caused by Sharkey and his cohorts. The seed grows into a mallorn tree, a rare and beautiful tree that brings joy and shade back to The Shire.
Did Galadriel see the devastation of The Shire even before the Fellowship had left Lothlorien? It is entirely possible that she did see such an event in her Mirror and, not having the power to stop it, she gave Sam the power to heal it.
So, why didn't Sam open the box before that time? One can only assume that Sam being so strong on faith and small on self-confidence had assumed that the box had contained exactly what Lady Galadriel had said it would but did not wish to lose such a precious thing. It may also be that with everything else going on, a box of dirt, no matter who it was a gift from, did not warrant much thought until the right moment.
Sam's gift from Galadriel is seen by many as part of Tolkien's stand on the environment. Long before it was an organized movement, Tolkien was a die hard environmentalist. The souring of The Shire was regarded as his wish for England itself.
Despite what Galadriel says, Sam's gift is far from a small one. Sam's gift was one that helps to truly make the end of the story a happy one, where even the after effects of a horrible war can be wiped away in the matter of only a single growing season.