From Heaven's Vantage
“One who prays should direct his eyes downward and his heart upward.” (Rambam, Laws of Prayer 5:4)
The heart represents the place of one’s concentration. This idea can be seen in a common expression, “To place one’s heart on the matter.” An instruction to direct one’s heart upward implies that one should concentrate on his prayers, directing them to
The instruction to direct one’s eyes downward towards the ground is in order for the worshipper not to be distracted. Since a person’s thoughts are affected by what he sees, if he would be looking straight ahead he could become distracted from his prayers by the various things happening around him. This is the straightforward meaning of the above instruction.
Regarding “directing the eyes upward”, the students of Rabbeinu Yona understood this as an instruction to banish all physical and worldly pleasures from the heart, and the person praying should try to envision himself standing in the Heavens above. Likewise, the Rambam writes that during prayer one should see himself as if he were standing in Heaven. (Mishneh Torah, Laws of Prayer, chapter 5)
“…for you are dust and to dust you will return” (Gen. 3:19)
The mentioning of one’s “eyes” can be understood as a reference to the “mind’s eye”. This application of the term “eyes” is similar to the usage of the phrase “to look”, as is found in “The Ethics of the Fathers (2:1 and 3:1): “Look (ponder) three things…” With this thought we will appreciate the following idea.
One of the implications in directing the mind’s eye downward towards the ground is in order to remind a person that his physical body originates from earth, to where he will inevitably return one day. In contrast to this, the heart is directed upwards to remind a person that his main concern should be for his soul, which comes from beneath
With the above in mind the worshipper will be reminded to pray for the soul, which is eternal and what is truly important, instead of just asking for material things, which can in the end be damaging for the person.