The Land of Israel as the Beloved of the Jewish People

At the beginning of Parshat Va'ayra, when addressing Moshe, Hashem employs the famous five leshonos of geulah in promising that He will liberate Bnei Yisroel from Mitzraim. In pasuk 6:8, we have the final expression of geulah:

"V'hayvayti etchem el ha'aretz asher nasati et yadi latet otah l'Avraham, l'Yitzchak, u'l'Yaakov, v'natati otah lachem morasha, ani Hashem."

That is, Hashem promises that He will bring B'nei Yisroel to the land that he promised to the Avos, and He will give Eretz Yisroel to the Jewish people as a "morasha."

Traditionally, the word "morasha" is translated as an "inheritance." (note: in Devarim 33:4, the Torah is also referred to as a "morasha" of the Jewish people).

In several places, the Gemara says the word "morasha" should be read metaphorically as "me'urasa" - i.e., betrothed - from the concept of "erusin", which is the first step in a Jewish marriage. 

What is the significance of this metaphorical reference?