General understanding:
* Comprehension
* Knowledge
* Awareness
* Grasp
* Perception
* Insight
* Apprehension
* Cognition
* Realization
* Enlightenment
Empathy and emotional understanding:
* Sympathy
* Compassion
* Sensitivity
* Empathy
* Feeling
* Connection
* Rapport
Intellectual understanding:
* Reasoning
* Logic
* Analysis
* Interpretation
* Explanation
Specific types of understanding:
* Agreement
* Consensus
* Harmony
* Concord
* Acceptability
* Acceptance
Informal words:
* Get
* Catch on
* Figure out
* See
* Know
The best choice will depend on the specific context and what you want to emphasize.