It says in the Midrash (Bereishit Rabbah 71:3):

R. Yitzchak says: "Rachel was 'akara' (barren) (Bereishit 29:31) – Rachel was the 'ikar' (the basis) of the home.

R. Shimon b. Yochai teaches: Since everything is dependent on Rachel, Am Yisrael were named after her: "Rachel weeps for her children." (Yirmiya 31:14). Not only [are they named] after her name, but also after the name of her son: "Then perhaps Hashem, G-d of Legions, will grant favor the remnant of Yosef. (Amos 5:15) Not only [are they named] after the name of her son, but also after the name of her grandson: "Is Ephraim my favorite son." (Yirmiya 31:15)

How does the word 'akara' (lit., 'barren'), which denotes something negative – having no children, change to 'ikar' ('basis'), which is positive – the basis of Am Yisrael?

On the pasuk: "The name of the bigger one was Leah and the name of the smaller one was Rachel" (Bereishit 29:16), Chazal teach:

"The name of the bigger one was Leah" – Bigger in her gifts: eternal priesthood and eternal royalty.

"The name of the smaller one was Rachel" – Smaller in her gifts: temporarily Yosef, temporarily Shaul and temporarily Shilo: "He rejected the tent of Yosef and did not choose the tribe of Ephraim." (Tehillim 78:67)

We learn from the Midrash that eternal things, such as priesthood and royalty, came from Leah, whereas temporary things came from Rachel. If Rachel was the basis of the home, why was she not the one to receive eternal gifts?

Yaakov Avinu's attribute is "tiferet" (glory). This attribute is combined of two other attributes – the attribute of "chesed" (kindness) and the attribute of "gevura" (courage), which is why he married two wives. Rachel (lit., lamb) is the attribute of kindness, and, like her namesake, is as gentle as a lamb: "Like a lamb silent before her shearers." She is always compliant, and sacrifices herself before her sister. Leah, on the other hand, represents the attribute of courage. Her name is like the pasuk: "nileati hachil" – a burden upon me." (Yeshaya 1:14) She struggles and fights to attain her will: "Leah went out to meet him." (Bereishit 30:16) Her daring and aggressiveness embodied the attribute of courage.

Rachel's role was to prepare the path for Leah. She paved the way for her sister without receiving the fruits of her labor. Yaakov wished to marry Rachel: "Yaakov loved Rachel" (Bereishit 29:18), but Rachel gave the signs to Leah so that Yaakov married Leah first. Rachel did not even get to be buried with Yaakov. She was buried on the road, while Leah, "the hated one," got to be buried in Me'arat Hamachpela with Yaakov. Rachel, through her torment and suffering, paved the way to victory, but the victory itself was attained by Leah.

Since the attribute of kindness is the foundation upon which the attribute of courage is built, this process repeated itself again with Yosef and Yehuda. Rachel's son, Yosef, was a dreamer: "Behold! The sun, the moon, and eleven stars were bowing down to me." (Bereishit 37:9) This was supposed to show that he would be G-d's Mashiach; he would be the king. However, in the end, he went down to Egypt and paved the path for his brother, so that the person who received the crown was Yehuda, Leah's son.

This is because royalty has to derive itself from the attribute of courage, whereas  Yosef had the attribute of kindness, and therefore deserved to be the "'nezir' (i.e., crown) of his brothers." He paved the path for Yehuda to receive the royalty in the same way that his mother prepared the path for Leah to build Knesset Yisrael, because the attribute of courage derives its strength from the attribute of kindness.

This is the prayer that we say in Shacharit: "Song and praise, lauding and hymns ... praise and splendor, holiness and royalty." Royalty draws its strength from holiness. Royalty is courage; holiness is kindness. Rachel's son, Yosef, who was "'nezir' of his brothers" – holiness, paved the path for his brother Yehuda, Leah's son, whose blessing was: "You, your brothers shall acknowledge ... your father's sons will prostrate themselves to you" (Bereishit 49:8) – the attribute of courage.

This explains how Rachel, who was barren, was the basis of the home. She was barren in the sense that she did not reap the fruits of her labor; everything with her was temporary. Rachel paved the way and laid the foundation, and this is the basis of the home. She was the foundation of the entire house of Israel, but did not reap the fruits of her labor. The process repeats itself in later generations. Yehoshua, from the tribe of Yosef, one of Rachel's sons, brought Am Yisrael into Eretz Yisrael, whereas Gideon from the tribe of Menashe, Leah's son, saved them in their time of need. Shaul, as well – who was from the tribe of Binyamin, one of Rachel's sons – was the first step towards the monarchy of the house of David – who came from Yehuda, one of Leah's sons – and was an eternal dynasty. Finally, Mashiach ben Yosef will prepare the path for Mashiach ben David, may he arrive soon!