General understanding:
* Understand
* Grasp
* Perceive
* Apprehend
* Seize
* Realize
* Know
* Get
* Figure out
* Make sense of
* See
* Discern
More formal or intellectual:
* Assimilate
* Cognize
* Envision
* Embrace
* Comprehend
* Appreciate
The best synonym to use will depend on the specific context and the desired level of formality.