Knowledge of Existence and Comprehension of Essence
Knowledge of Existence is when one knows about the existence of something from external sources (like understanding one thing from another), and Comprehension of Essence is when one knows the thing itself - its essence.
In Human Understanding
Knowledge of Existence means that one knows about a certain reality that exists, but has no recognition of its essence. That is, when recognition comes through personal perception (for example through hearing), it's possible that a greater scholar might come and contradict their understanding.
Comprehension of Essence is when one recognizes the essence of the thing. One of the ways in which this matter is very prominent is - in seeing. Meaning, when recognition comes through sight (seeing the matter for oneself), it is impossible to convince them otherwise with any explanation. They don't arrive at this through a subjective perception of the matter, but simply see the thing itself.
From our perspective, since we live in a physical world, the only things we can grasp in their essence are physical things that exist in our world. Spiritual things - we can only grasp their existence, the fact that they exist.
In Divine Service
Our knowledge of Hashem today is merely knowledge of existence, which is why the Torah commands the mitzvot using the language of hearing: "Hear O Israel," "And now hear the statutes" - and not as Moses requested "Let me cross over and see."
But in the future (and also now in Gan Eden) there will be true recognition of the essence of G-dliness in a manner of actual seeing, as it is written "As in the days of your exodus from Egypt, I will show him wonders."