Terminologycally Imam Nawbi RA said that, having a strong desire for any work is called intention or Niyyah. (Faizul Qadir, Volume I, Page No. 30)
No act of worship is accepted to Allah SWT except Niyyah. Because the Prophet (peace and blessings of Allaah be upon him) said,
إنَّمَا الأعْمَالُ بِالنِّيَّاتِ وَ إنَّمَا لِكُلِّ امْرِىءٍ مَا نَوَى
Meaning: The reward of deeds depends upon the intentions and every person will get the reward according to what he has intended. - Sahih al-Bukhari 1
Niyyah is required for every act of worship to be pure. Niyyah is also required at the beginning of the great act of worship like Hajj or Umrah.
And the intention is to decide something in the heart. And that is only the work of the heart, so in case of any intention of worship, it is not necessary to utter Arabic words.
Yes, if one's mind is not fixed without uttering his intention, then he can utter the words of intention in his mouth.
In this case, it is enough to pronounce in one's own language, there is no need to repeat long and wide Arabic sentences - (Fathul Qadir 1/26).
Hajj and Umrah pilgrims will clean the fingernails, mustache, and navel and armpit hair before Ihram. Then take a bath and wear Ihram clothes. Those who perform Hajj will Niyyah to perform Hajj and those who perform Umrah will Niyyah to perform Umrah.
Hajj and Umrah will be the Niyyah of the performer for either of these two acts of worship. This Niyyah is verbally agreed with the Shari'ah. Here are the Niyyah of Umrah and Hajj:
If you're performing Umrah at any time of the year, or Umrah as part of Hajj al-Tamattu, you should make this Niyyah. Later, another Niyyah is made for Hajj al-Tamattu.
لَبَّيْكَ اللَّهُمَّ عُمْرَةً
Labbayk Allahumma Umrah.
O Allah, here I am to perform Umrah.
اللَّهُمَّ إِنِّيْ أُرِيْدُ الْعُمْرَةَ
Allahumma Innee Ureedul Umrah.
O Allah, I intend to perform Umrah.
اللَّهُمَّ إِنِّيْ أُرِيْدُ الْعُمْرَةَ فَيَسِّرْهَا لِيْ وَتَقَبَّلْهَا مِنِّيْ
Allahumma Innee Ureedul Umrata fa-Yassirhaa lee wa Taqabbal-haa Minnee.
O Allah, I intend to perform Umrah, so accept it from me and make it easy for me.
If you're performing Hajj al-Tamattu (after Umrah) or Hajj al-Ifrad, you'll need to make this Niyyah (only Hajj).
لَبَّيْكَ اللَّهُمَّ حَجًّا
Labbayk Allahumma Hajj.
O Allah, here I am to perform Hajj.
اللَّهُمَّ إِنِّيْ أُرِيْدُ الْحَجَّ
Allahumma Innee Ureedul Hajj.
O Allah, I intend to perform Hajj.
اللَّهُمَّ إِنِّيْ أُرِيْدُ الْحَجَّ فَيَسِّرْهُ لِيْ وَتَقَبَّلْهُ مِنِّيْ
Allahumma Innee Ureedul Hajja fa Yassir-hu lee wa Taqabbal-hu Minnee.
O Allah, I intend to perform Hajj, so make it easy for me and accept it from me.
If you're performing Hajj al-Qiran, you should make this Niyyah (Umrah and Hajj together).
لَبَّيْكَ اللَّهُمَّ عُمْرَةً وَ حَجًّا
Labbayk Allahumma Umratan wa Hajj.
O Allah, here I am to perform Umrah and Hajj.
اللَّهُمَّ إِنِّيْ أُرِيْدُ الْعُمْرَةَ وَ الْحَجَّ
Allahumma Innee Ureedul Umrataw-wa Hajj.
O Allah, I intend to perform Umrah and Hajj.
اللَّهُمَّ إِنِّيْ أُرِيْدُ الْعُمْرَةَ وَ الْحَجَّ فَيَسِّرْهُمَا لِيْ وَتَقَبَّلْهُمَا مِنِّيْ
Allahumma Innee Ureedul Hajja fa Yassir-hu lee wa Taqabbal-hu Minnee.
O Allah, I intend to perform Umrah and Hajj, so make them easy for me and accept them from me.
The Prophet (peace and blessings of Allaah be upon him) Niyyah to do so. Those who go out in ihram for the purpose of Hajj or Umrah, they are in the car or plane or any other vehicle; It is better to utter the words of Niyyah mentioned while boarding the vehicle after Ihram.
May Allaah give the Muslim Ummah strength to perform the Sunnah by uttering the Niyyah in the Ibadah of Hajj and Umrah. Amen.