This is one of those chapters that really just need to be read in its fullness. It was thoroughly thought provoking when it brought to light some of the ways that Samuel, Saul and David recapitulate the books of Genesis and Exodus.
But more importantly, and on the subject of the Eucharist, the story of David on the run from Saul stands as the sabbath supper example. As Dr Leithart points out allowing David to eat the Showbread was an informal deceleration by God that David was a part of His anointed household.
This might at first seem questionable but it sheds some valuable light on Psalm 2 and Psalm 110. But are used in Hebrews to defend the priestly anointed of Jesus Christ. The same Jesus Christ who is the promised descendant of David. David was brought into the house as an example pointing to his Son Jesus.
But the story also speaks to us. We have been made priests. We have received anointing. And we are called to celebrate the provision of the Showbread as a sign that we truly are the chosen house of God set to serve before Him.