Du'aa' has a very strong relationship with one's 'aqeedah (creed) [عقيدة, plural: 'aqaa'id عقائد] and tawḥeed [توحيد]. Du'aa' is also one of the best ways that a person can increase his eemaan (faith) [ايمان] , and appreciate Allaah's Names and Attributes. It is a powerful reminder of man's inherent incapability, and Allaah's unlimited powers.
Du'aa' increases a person's eemaan due to many factors. It makes evident the fact that a person has absolutely no control over his destiny, nor does he have the power to benefit himself or avert any evil from him. It shows the neediness that a Muslim feels towards his Lord. It proves that the one making du'aa' sincerely believes that Allaah سبحانه و تعالى hears his du'aa', and will respond to it. Such a person must also affirm Allaah's Infinite Mercy, Beneficence and Generosity. And the more a person increases in the realisation of his poverty towards the Mercy of his Lord, the more he will increase in his eemaan as well. Likewise, the more a person appreciates and realises the perfection of Allaah's Names and Attributes, so too will he increase in his eemaan. These two factors - knowing one's need of Allaah سبحانه و تعالى in every matter, and knowing Allaah's Perfect Nature - are the essence of eemaan and servitude to Allaah سبحانه و تعالى.
The one making du'aa' openly affirms his eemaan for Allaah سبحانه و تعالى, for it shows that he believes in Allaah سبحانه و تعالى, and that Allaah, and only Allaah, can listen and answer his prayers.
Another way in which the importance of du'aa' can be demonstrated is by showing that du'aa' is an implicit affirmation of tawḥeed in all of its aspects.
When one makes a du'aa' to Allaah سبحانه و تعالى, one is implicitly acknowledging that Allaah سبحانه و تعالى exists, and that He is the true Lord. The person so doing is stating by his actions that Allaah سبحانه و تعالى controls all matters, for only Allaah سبحانه و تعالى has the power to respond to his du'aa'. He is admitting that Allaah سبحانه و تعالى is the Nourisher, Sustainer, Creator and Master of the entire creation, and all of this is the essence of Tawḥeed ar-Ruboobiyyah [توحيد الربوبية].
Even when a non-Muslim makes a du'aa' to Allaah سبحانه و تعالى (even if it is by another name), he affirms all of these concepts as well. It is because of this affirmation that it is possible that a non-Muslim's du'aa' is answered as well, for the response of a du'aa' related to Tawḥeed ar-Ruboobiyyah. Allaah سبحانه و تعالى mentions in numerous verses in the Qur'aan (some of which will be mentioned later) that disbelievers call out to Him at times of need, and yet, when He responds to their du'aa', they worship others besides Him. So the point is that Allaah سبحانه و تعالى does respond to the du'aa' of the kaafir (unbeliever) as well as the Muslim, for both turn to Allaah سبحانه و تعالى recognising that only Allaah سبحانه و تعالى can grant them what they desire. However, the du'aa' of the Muslim has a greater chance of being accepted, for he calls out only to Allaah سبحانه و تعالى, whereas the kaafir calls out to others besides Allaah سبحانه و تعالى, turning to Allaah سبحانه و تعالى only when he is in great distress. Also, the fact that Allaah سبحانه و تعالى responds to the du'aa' of the kaafir does not in any way imply that He is pleased with him, or that he will be saved from the fire of Hell. Rather, it shows that Allaah سبحانه و تعالى is the Rabb, the true Lord of both the Muslim and the kaafir, and it shows that He is ar-Raḥmaan, the Ever-Merciful, for He shows Mercy to the Muslim in this life and the Hereafter, and He shows some Mercy to the kaafir in this life. Were it not for this Mercy, the kaafir would even be blessed with a morsel of food or a sip of water. And this general mercy entails that Allaah سبحانه و تعالى responds occasionally to the du'aa' of a kaafir, especially when it emanates from a heart that has turned sincerely and desperately towards Allaah سبحانه و تعالى.
Du'aa' also necessitates that only Allaah سبحانه و تعالى deserves to be worshipped (Taḥeed al-Uloohiyyah) [توحيد الألوهية], for if only Allaah سبحانه و تعالى has complete control over creation, and if only He can respond to the call of the one in distress, then only He deserves our complete submission and worship.
Du'aa' also obligates that Allaah سبحانه و تعالى has the most Perfect Names and Attributes (Tawḥeed al-Asmaa' was-Ṣifaat) [توحيد الأسماء والصفات]. For only He can hear the whispering plea of the servant, no matter where the servant is, and only He can understand the situation that the servant is in. His knowledge is far more complete than the knowledge of the servant himself concerning the plight that he is in. Likewise, only Allaah سبحانه و تعالى has the complete power and ultimate authority in granting what the servant desires.
So du'aa' is a powerful indication of Tawḥeed in all of its three aspects.
[Dua: The Weapon of the Believer]