To "feast" is to partake of a sumptuous meal. A feast is a banquet, principal or ample meal. A feast is also defined as a religious anniversary observed with rejoicing.
Figuratively, to feast is to experience delight or gratification to the mind or senses. The root of the word "feast" comes from a general root that refers to religious holidays or other religious activities or concepts. Its Greek root has the sense of things "of the gods." It comes from the same root as words that refer to temples and ceremonial meals connected to the temple.
As is often the case, in the scriptures the words "feast" or "feasting" are translated from a number of different Hebrew and Greek words. But relevant here, the Hebrew word has the sense of an appointment, or fixed time or season. Specifically, feast is related to a festival or assembly convened for a definite purpose.
Technically the word also means "the congregation," but by extension it means the place of meeting or a place of solemn assembly, congregation or solemn feast. Another sense from Hebrew is the renewal of religious services or a dedication. Of course, it also means a dinner or cake or the chief meal.
The Greek root of the word means "victim," meaning a solemn feast day defined by sacrifice and solemnity. It also has the sense of marching in a sacred procession or celebrating a festival.
It is arresting to think of the biological image contained in "feasting upon the word of Christ." Of course, one aspect of this is simply biological to eat, to absorb. For example, the apostle John was commanded to take a book from the hand of an angel "and eat it up" (Revelation 10:9). Ezekiel was commanded to "eat this (scroll), and go speak unto the house of Israel" (Ezekiel 3:1). Also, Jeremiah tells us "thy words were found, and I did eat them; and thy word was unto me the joy and rejoicing of mine heart: for I am called by thy name, O Lord God of hosts" (Jeremiah 15:16).
When we combine the notion of ingesting and absorbing the words of scripture with the idea that this is a holy meal, it gives us an idea how to approach our study of the scriptures.
We cannot approach the scriptures casually or treat them as though we were reading another book. "Those who delve into the scriptural library find that to understand requires more than casually reading or perusal. There must be concentrated study" (President Howard W. Hunter, Ensign, November 1979).
President Ezra Taft Benson, who taught us much about immersing ourselves in the scriptures, teaches us that "there is a power in the Book of Mormon, which will begin to flow into your lives the moment you begin a serious study of the book" (Ensign, November 1986).