This word comes partnered with "eil" (P21) in the Amidah.
We are actually very familiar with another form of this word –"aliyah." We know it from the synagogue service, in which aliyah means going up to the bima for an honor, and we know it from the mitzvah of living in the Land of Israel, in which aliyah means moving to the land itself, to the "high ground" both literally and symbolically.
Another form of this word is a kind of sacrifice – olah – whose smoke and aroma rises upward.
So, obviously, the idea behind elyon is going upward. And, indeed, the translation of the word is "most high." Eil elyon is "most high God."
It is somewhat natural when we "look" for God that we raise our eyes toward the sky. In language and literature, whether literally or figuratively, we imagine God in a geographic location above us, and perhaps even above what is above us. However, we know that there is no geography to God, and the notion that the Most High God is a physical presence beyond the clouds is both foolish and unsatisfying.
To accept an aliyah in synagogue, one must leave her place and come close to the Torah or the Ark. To make aliyah by moving to Israel, one must uproot himself for the sacred to fulfilling a holy obligation. And to offer an olah, some that is pleasing and of great value must be sacrificed.
These are the attributes of our God, who calls us to "higher" purpose – to shake loose our sedentary lives and draw nearer to the source of Torah, to leave the comfortable and familiar in order to fulfill mitzvot, to dedicate that which is pleasing and valuable (not undesirable and expendable) to divine service.
There use of spatial adjectives for God and for worthy purposes is probably too ingrained to be abandoned, but never too common to by properly understood. Eil elyon inspires us to believe that our grasp can exceed our reach.