Gemara: [The malach hamavet (angel of death) needed to take David, who was pushing off his impending death by his involvement in Torah study]. David had an orchard behind his house. The malach hamavetwent up and shook the trees. David went out to see. He was climbing a ladder. A rung fell out from beneath him. He was silenced, and he died.
Ein Ayah: The external events that transpired in this story were fitting for the inner nature of the great and holy spirit of David at that very special time [of his death].
When a person is involved in conceptions that are limited enough that he can access them well with his senses, he does not feel that he is in a confined place. However, when he elevates himself to higher and broader conceptions in matters of the divine that captivate a holy heart, then he feels his physical location is too constricting. Walls that surround him will make him uncomfortable, and he will want to go out to the free spaces outside a building.
The orchard that was outside David’s house was appropriate for contemplation about things that were beyond the boundaries of the senses, just as the house was the correct place to delve into those things that are within the limited boundaries of the senses. When that which occupied David was beyond those confines, he went outside.
In the case at hand, the cause of the need to go outside was the need for David to die an especially uplifting death (known as the death of a kiss). In that context, the malach hamavet went up and shook the tree. In order to enable the physical death of the anointed of Hashem, David was caused to focus on such lofty ideas that they required him to leave the confines of his house. That is what is meant by his going out to see that which was "blowing around" in the orchard, i.e., those contemplations for which breadth and the ability to spread out were appropriate.
The gemara then describes how David was climbing a ladder, which represents his reaching from one intellectual/spiritual level to the next one. Finally he reached such a point of fullness and divine connection that the weak powers of the body could no longer hold the spirit that desired to leave its physical framework. The spirit felt at that point that the body was just an impediment to its ability to grasp and for his spirit to cling to Hashem’s light. That is what the gemara means by a rung falling from beneath him. It fell because it was beneath his level, and it was holding him back from further elevation.
At that point, David also felt that the power of speech was too limited to contain all the divine pleasantness that he was able to grasp. That is the reason that he was silenced at death. This is the manner of lofty, holy individuals who "laugh" on their final day. Their spirit leaves their body in a display of holiness, full of pleasantness and a great love of the Creator of the Worlds, their Father in the Heaven.