Marriage talks or a marriage proposal; discussions or arrangements regarding a marriage (often formal or traditional).
両親が私の縁談について話し合っているらしい。
It seems my parents are discussing a marriage proposal for me.
彼女は縁談の話を断った。
She refused the marriage proposal/talks.
昔は縁談で嫁や婿が決められることも多かった。
In the past, brides and grooms were often decided through arranged marriage talks.