Marriage Proposal
Marriage Arrangements, Marriage Discussion
noun
You learned 縁 means "edge," but remember how it can also mean "relation"? Well, when you have a relation to discuss, that can only mean one thing: it's marriage proposal time! Er, that was the direction you were hoping to take this relation, right? Hope so…
縁談 is a relatively formal word for the discussion, suggestion, arrangement, or proposal of marriage, often in the context of matchmaking or arranged marriages. It's not for the actual act of proposing — for that you'd just use プロポーズ.
This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own.
高卒以下の学歴の男との縁談を私に持って寄越すなんて、一体どういう神経してる訳？
How dare you to bring me a marriage proposal from a guy who has less than a high school education?!