to understand: to put the pieces together in the mind and grasp what something means
This verb pictures understanding as a kind of assembling. Its parts mean to bring together, so it names the moment when scattered facts, words, or events suddenly connect and their meaning becomes clear. It is close to the English idea of catching on or seeing how it all fits.
In the Gospels it clusters around one recurring situation: people hear Jesus but fail to grasp him. The disciples do not understand the passion predictions or the meaning of the loaves; the crowds hear the parables without comprehending them. Behind much of this stands a line from the prophet Isaiah, quoted several times, about people who hear but never understand and see but never perceive. In that setting the word carries more than intellectual effort: it is the perception that only an opened heart can reach, which is why one Gospel scene has Jesus opening the disciples' minds so they can understand the Scriptures.
So the word runs from ordinary comprehension (grasping what a saying or event means) to the deeper discernment of God's ways that dull or hardened hearts miss. It is the same act of grasping throughout; what changes is what is being grasped and whether the hearer is truly able to.