In his first stanza, Ronald Arbuthnot Knox sets the scene
There was a young man who said "God
Must find it exceedingly odd
To think that the tree
Should continue to be
When there's no one about in the quad."
A young man is thinking about a quad that he is familiar with
A quad or quadrangle is an area surrounded on four sides by buildings in an academic setting and usually part of a larger campus
from this one can infer that the young man may be a student or scholar.
The question is asked whether the tree should be / exist or not if no one is present. The reference is not to a tree but the tree.
metaphorically the tree is an allusion to the tree of knowledge
This is a philosophical question along the lines of
If a tree falls in a forest (note parallel using tree)
In his second stanza, Knox writes God's reply
Dear Sir: Your astonishment's odd;
I am always about in the quad.
And that's why the tree
Will continue to be
Since observed by, Yours faithfully, God.
God's reply is that (s)he is always present (always about in the quad) and therefore the tree lives (continues to be). (S)he closes using observed and faithfully
Observance and faith are religious codes words for piety.
On the surface the limerick is saying God is ever present.
At a deeper level, Knox may be saying that
God knows more than man can comprehend
no matter the learned education
Knox's writings are considered to be witty and eloquent and usually calls into question Catholic doctrine.