In his prayers a Muslim, due to his good morality, wants everything good that he wants for himself, also for his brothers.

In his prayers a Muslim asks Allah for goodness both in this world and in the Hereafter. He prays Allah to be able to be the servant He loves and approves most.  He wants to be the closest to Allah among all the people ever existed; to be able to love Allah with the biggest love a person could ever feel.  He would want to be the servant who appraises Allah as is due the most among all people. He would want to behave in the manners most approved in the Presence of Allah and to have a morality Allah would love the most. He would want to be Allah's servant who thanks Allah the most, who is able to appraise His blessings the most. He would want to be the one who has assumed the morality of Allah the most and the one who Allah manifests His Names the most. He would want to be the person who could understand and practice the verses of the Qur'an the most.  He would want to be the person who abides by all the commands and prohibitions Allah revealed in the Qur'an most perfectly and most fastidiously.  He would want to be the person who could communicate the religion of Allah in the most beautiful, the most effective, most sincere manner.  He would want to be the one, who is blessed with being the person strives the most, in the way of Allah, with all his possessions and with his life.  He would want Allah to make him spiritually and physically the most healthy, most powerful, the strongest person on earth and thus be able to serve Allah the most with all his strength.  He prays to be able to do all he does in the most sincere manner possible.  He would want to be able to submit to Allah with all his soul and body with the most profound submission ever possible. He would pray to be the person who could respond to the shortcomings Allah created with the most thankful, most trusting, most patient and best morality. He would want to be the person who fears Allah with the most profound fear. He would want to be the person who could keep his hope from Allah in the highest level, the one who trusts Allah the most, the one who never doubts and the one who is most sure of Allah's help even in the hardest times. He would want to be the one who keeps away the most from ascribing partners to Allah, who never turns to anyone else other than Allah, who conceives the fact that there is no god but Allah most profoundly. He would want to be the most preeminent person in good morality; he would want to be the most loving, most respectful, most compassionate and most merciful, most complaisant, most forgiving, most gracious, most self-sacrificing, most selfless, the kindest, the most hospitable, the most easygoing, the most contented, the most patient, the most understanding, the most well disposed, the most trustworthy; he would want to be the one who gives the most joy, happiness, peace and easiness; the one who speaks the best;  the one who gives the best advises; the one who is most compliant to the advices; the one who obeys the most.   He would want to be the person that all the Muslims in the world loves the most, respects the most, trusts the most, the one with whom they would want to be with the most, the one whose conversation they delight in the most, the one whose words they trust the most, the one whom they would want to be with the most in this world and eternally in the Hereafter. He would want to be rewarded with the most beautiful rewards Allah bestows in the Hereafter; to be the one who Allah raised up the highest. And by being the servant of Allah who He approves the most, who has been blessed with being the closest to Allah; he would want to be rewarded with the greatest blessings of Allah in the most beautiful Heavens. 

Muslims would want to attain "the highest possible rank" in all these beautiful blessings. However as the requisite of the understanding of love and sincerity they learnt from the Qur'an, they want all these blessings and beauties "in the highest possible rank" for their brothers as well.  Just like their desire to be the one closest to Allah; to be the servant that Allah loves the most; they would want their Muslim brothers to be among the ones Allah loves the most and made most preeminent in closeness to Allah.  For that reason in all their prayers they pray not by saying "me" but by saying "us". They pray by saying "Give us all those blessing my Lord", instead of saying "Give me all those blessings my Lord". When a Muslim prays for them with a good will, they respond with the exact same manner. For instance when someone says "May Allah give you a nice day", such a Muslim would respond by saying "May Allah give us all a nice day." In the same manner when one says "May Allah be pleased with you" he would respond by saying "May Allah be pleased with all of us." 

This is a morality that a person, who wants to be the most preeminent in faith, to be the best example to the ones fearing Allah; a person who loves Allah the most, would assume.  Consequently this kind of morality he displays in his prayers is a very important indication for his faith, his love for Allah, his fear for Allah, and his sincerity and depth.

In the Qur'an Allah had given many examples of the prayers of Muslims that display such morality. Some of those examples are as follows:
 

.. You alone we worship.You alone we ask for help.

Guide us on the Straight Path;

the Path of those You have blessed, not of those with anger on them, nor of the misguided. (Surat Al-Fatiha: 3-7)
 

And there are others who say, ‘Our Lord, give us good in the world, and good in the Hereafter, and safeguard us from the punishment of the fire.’ (Surat Al-Baqara: 201)
 

Allah does not impose on any self any more than it can stand. For it is what it has earned; against it, what it has merited. Our Lord, do not take us to task if we forget or make a mistake! Our Lord, do not place on us a load like the one You placed on those before us! Our Lord, do not place on us a load we have not the strength to bear! And pardon us; and forgive us; and have mercy on us. You are our Master , so help us against the people of the unbelievers. (Surat Al-Baqara: 286)
 

"Our Lord, do not make our hearts swerve aside after You have guided us. And give us mercy from You. You are the Ever-Giving." (Surat Al'Imran: 8)   
 

Those who say, ‘Our Lord, we have faith, so forgive us our wrong actions and safeguard us from the punishment of the Fire.' (Surat Al'Imran: 16)
 

Those who remember Allah, standing, sitting and lying on their sides, and reflect on the creation of the heavens and the earth: ‘Our Lord, You have not created this for nothing. Glory be to You! So safeguard us from the punishment of the Fire'. (Surat Al'Imran: 191)