Meaning of Khushu` and How to Develop It in Prayer
Question

Is it true that if a prayer is lacking in complete khushu` (focus of mind and humility before Allah), He will not accept it from us?
Praise be to Allah.Meaning of Khushu`
What is required of the worshipper is to show humility [khushu`] in his prayer and to have complete focus of mind, because Allah, may He be exalted, says (interpretation of the meaning):
“Certainly will the believers have succeeded:
“They who are during their prayer humbly submissive [khashi‘un].” [al-Muminun 23:1-2]
Focusing on prayer and being humble therein are among the most important issues, and this is the essence of the prayer. Therefore we must pay attention to focusing with proper humility in the prayer and performing it in a tranquil and unhurried manner, when prostrating and bowing, between the two prostrations, and after bowing when standing up again; it should be done in a tranquil and unhurried manner.
Is prayer valid without khushu`?
If the worshipper fails to focus his mind and show humility in such a way that it is as if he is pecking his way through the prayer and is too hasty, then his prayer becomes invalid.
But if he is at ease and performs his prayer in an unhurried manner, but sometimes his mind wanders and sometimes he forgets, this does not render his prayer invalid, but he will not have any reward for his prayer except inasmuch as his mind was focused and he showed proper humility and mindfulness of Allah; he will have the reward for that, but as for the parts in which he was not focused, he will miss out on the reward thereof. Therefore he should focus on his prayer and do it in an unhurried manner, showing humility towards Allah, may He be glorified and exalted, so that he will have the reward thereof in full. But his prayer is not rendered invalid unless he prays in a hasty manner, such as if he bows but does not take the time to do it properly, so he does it in a hasty manner and the movement does not reflect proper humility. What he should do is move with ease, so that he adopts the right posture with every vertebra in place and so that he will have enough time to say Subhana Rabbiy al-‘Azim (Glory be to my Lord the Almighty) when bowing and to say Rabbana wa laka’l-hamd (my Lord and to You be praise) when standing up straight after bowing, and to say Subhana Rabbiy al-A‘la (Glory be to my Lord Most High) when prostrating, and to say Rabb ighfir (Lord forgive me) between the two prostrations.
How Prophet Muhammad advised the man who didn’t pray in a calm manner
When the Prophet (blessings and peace of Allah be upon him) saw a man who did not pray in a calm and unhurried manner – rather he pecked his way through the prayer – he instructed that man to repeat his prayer, and said: “Pray, for you have not prayed.” Praying in a calm and unhurried manner is one of the most important aspects of khushu` , and this is something that is required in the prayer, when bowing and prostrating, between the two prostrations, and when standing up straight after bowing. This is called tumaninah, which means being calm and at ease, proceeding in an unhurried manner. It is also called khushu` , which means having proper focus and humility when praying. It is essential to pray in this calm and unhurried manner, so that at every stage of the prayer, the vertebrae may settle into place. So when the worshipper bows, he should do so in an unhurried manner, so that every part of his body may settle into place, and when he stands up from bowing, he should do it in such a manner that every vertebra will settle into place when he is standing after bowing; and when he prostrates, he should do it in a calm and unhurried manner, and should not be hasty, so that every bone may settle into place (as he prostrates).” (Shaykh ‘Abd al-‘Aziz ibn Baz (may Allah have mercy on him)
For more, please see this category: Conditions of Prayer
And Allah knows best.