It indicates the overcoming of natural scepticism.
There is no plain-vanilla—i.e., pa’al—version of the root a-m-n. In other words, there is no verb le-émon לֶאֱמוֹן. Belief is something that needs to be applied to oneself—the default mode is disbelief. (As they say in Missouri—’Show me.’)
Similarly, there is no verb for ‘going far’: when one simply goes, one holekh—but when one goes far, one marḥiq lekhet—lit. ‘make distance going’.
So when Abraham is persuaded that God will do all that He is promising, he is actively overruling his natural scepticism, to make himself believe.
That’s a beautiful analysis and interpretation of the subtlety of a grammatical element of the biblical passage. Thank you, Jonathan!