Towards the end of Parashat Ki-Teseh, the Torah presents the Misva of Yibum, which applies when a married man dies without children. His brother is required to marry the widow, and the child born from this marriage will be considered, in some sense, the offspring of the deceased. If the brother refuses to marry the widow, then he must perform a special ceremony called "Halisa," whereby he wears a special shoe which the widow removes from his foot. (Although it is clear from the Torah that Yibum is preferred over Halisa, nowadays, Halisa is performed when this unfortunate situation arises, for reasons which lie beyond the scope of our discussion.)
Various different approaches have been suggested to explain the meaning and significance of Yibum and Halisa. Rabbenu Bahya (Spain, 1255-1340) suggested, quite simply, that the Torah commands the brother to marry the widow in order to keep the deceaseds wealth in the family. Since the deceased had no children, his only inheritor is his wife, and if she would then marry somebody else, all his wealth would end up in a different family. As people generally wish for their wealth to remain in their family, the Torah commanded the brother to marry the widow.
In explaining the significance of Halisa, Rabbenu Bahya writes that Yibum has the effect of bringing the deceased back to life, in some sense. As the Torah writes, the child produced by the brothers marriage to the widow "shall be named after the deceased." Since the deceased in effect caused this child to be born, as his brother was required to marry the widow because of his death, the deceased who had no children is considered as having a legacy and presence in this world through the birth of that child. And so if the brother refuses to marry the widow, he essentially causes the brother to "die" again. He consigns the brother to no longer have any chance of leaving a legacy in this world. The brother therefore has his shoe removed a symbol of mourning, conveying the message that his refusal is causing his brother to "die" once again, in that it denies the brother an opportunity for a spiritual presence in this world through offspring.
But the removal of a shoe from the brothers foot might also send a different message.
The Zohar and other sources speak at length about a persons ability to elevate his fathers soul in the next world. By performing Misvot in the fathers merit, a person brings great blessing to the deceased fathers soul. In fact, a sons Misvot performed in the fathers merit have a greater effect upon the fathers soul than those performed by the greatest Sadik in the world. The Gemara teaches that one is required to honor his parents both during their lifetime and after their passing. When the parent is alive, the child is to help him here in this world by caring for him and respecting him. When the parent passes on, the child is to help the parent in the next world, through the performance of Misvot.
Elsewhere, the Gemara comments that a child is "Kara Deabu" "his fathers leg." The commentators explain this to mean that a child has the ability to enable his parent to "move" even in the next world. Once a person leaves this world, he no longer has the ability to perform Misvot, and so he no longer has the ability to build himself, to elevate himself, to grow and develop. The only way this can be done after death is through ones offspring, whose good deeds are attributed, to some extent, to the parent who produced the children and trained them to observe the Torah. The child is the parents "leg" in the sense that he grants his father the ability to continue "walking" even in the next world, to be elevated and raised, through the performance of Misvot.
This might be the meaning of the Halisa ceremony. The shoe is removed from the brothers foot to sharply reprimand him for denying his brother a "shoe" a child who would be able to carry his soul further in the next world. The Torah gave the brother the opportunity to produce a child that would be considered the child of the deceased, and would thus elevate the deceaseds soul to infinitely greater heights in the next world, but he chose not to seize this opportunity. He thus removed his brothers "shoe," his means of achieving greater elevation.
The greatest thing we can do for our beloved family members who have left this world is to involve ourselves in the study and observance of Torah in their merit, through which we elevate their souls to ever greater heights for all eternity.