understanding: the ability to see how things fit together and what they add up to, and the insight that comes with it
This noun belongs with the verb συνίημι, whose parts mean to bring together. That picture governs the noun: it is not the store of what a person knows but the act of putting pieces together and seeing what they mean. English "understanding" is close, though the Greek word leans harder toward discernment than toward general awareness.
The New Testament uses it in two directions. Sometimes it names the mental power itself, the quickness of mind others can notice and admire, as when the boy Jesus astonishes the teachers in the temple. Sometimes it names the grasp of one particular thing, as when Paul speaks of his own insight into the plan God kept hidden for ages. The two hang together, since the ability exists in order to be used on something.
In Paul's letters the word keeps company with two others. Wisdom (σοφία) is skill in living and ordering life well; knowing God personally (ἐπίγνωσις) is the relationship the gospel creates. Understanding sits between them as the discernment that works out what God's will means in a given case. Notably, Paul prays for it rather than assuming his readers already have it, which makes it something given rather than a natural talent.
Behind all of this stands the Old Testament. Greek-speaking Jews regularly used this word for the Hebrew term for understanding (בִּינָה), the discernment that Proverbs pairs with wisdom and treats as a gift worth searching for. Paul's quotation of Isaiah in 1 Corinthians 1:19 then turns the expectation over: the understanding of the clever is exactly what God sets aside at the cross.