Why do we pray? Our Rabbis gave many reasons, but this is not the place to list them. However, we will mention one reason, based on the words of Nachmonides (end of Parshat Bo), Miamonides (Guide to the Perplexed, Part 3, Ch. 36) and the Maharal (Netiv Ha’Avoda, Chapter 3). Let us examine the Maharal’s words:
Israel’s service to G-d, which they have in every place in exile, is prayer… and prayer is called service as we explained above, because the prayer that man prays to G-d shows that man is dependent on Him and needs Him and has no existence without Him…

The essence of prayer is to show G-d’s providence over us, and our dependence on Him and need of Him. For example, when a person requests a cure from G-d he is acknowledging that G-d is the Healer of His people Israel, and that salvation will emanate from Him. Prayer does not create a sense of awe of G-d, since its essence is not just to show G-d’s greatness (and when we do describe the greatness a distance is created as man’s insignificance becomes clear). On the contrary, prayer creates closeness; it shows that there is a connection between us and G-d, and G-d is the One Who cares for our needs.

Another reason can be seen in the Midrash in our Parsha, Parshat Toldot. The Midrash Rabba (Genesis Rabba 45; Tanchuma, Toldot 9) says:
Why were the matriarchs barren? Rabbi Levi in the name of Rabbi Shila of Kfar Tamarta, and Rabbi Chelbo in the name of Rabbi Yochanan said that G-d yearns for their prayer and their communication, as it says (Song of Songs 2) "My dove is in the clefts of the rock".

The matriarchs were therefore barren since G-d yearned for their prayers. This known midrash contains an amazing message! How is it possible that because G-d yearned for their prayers the matriarchs were barren? From here we can understand, that there is enormous significance to prayer. G-d knows that there is a need for man to pray, and G-d as the Source of good, wants us to pray to Him. And from here: there is a personal meaning to prayer, an attachment, a kinship. An encounter whereby one understands the dependency, and our will merges with G-d’s will. A meeting which is meant to repair and influence us. A meeting which imbues us with power in this world.

And so it emerges from the words of Rabbeinu Bechaya (Kad HaKemach, prayer, starting from G-d, L-rd):
It seems to me, that this shows that the barrenness is not the main reason, but rather prayer, and the condition of barrenness existed so that there should be prayer. If so, prayer is the essence!
Rav Kook explains (Olat RAYH) the special influence of prayer on man:
The difference between one who prays and one who does not pray, is not that the first designates an hour a day to his prayer and the second does not designate an hour for this purpose. There is a fundamental difference here. The lifestyle of these two is completely different: that hour of prayer imbues the whole day with a special effect. [Rav Kook, Orot Hatefila, p. 82].

One who prays influences his entire day. In our days we can compare this to the cell phone. Without charging – the cell phone stops working. We need daily charging, to connect with the King, to connect with the Source. A connection from which the whole day will be impacted.
And if so, one aspect of praying is to show that we are dependent on G-d. That we believe in His Providence and we know that everything in the world comes from His Might. But there is also another issue in prayer – prayer constitutes an encounter, connection, an embrace with G-d. This meeting, this dialogue gives us strength, and elevates, exacts and purifies our daily existence.