What is the source of the following the hadith?
“At the beginning of every century Allah will send to this ummah someone who will renew its religious understanding”
What does it mean? Is it pointing about Wali-ul-Allah?
Sources
The Prophet (ﷺ) said: Allah will raise for this community at the end of every hundred years the one who will renovate its religion for it. (Sunan abi Dawod)
The hadith was qualified as sahih by scholars such al-Hakim from Nishapur, his student al-Bayhaqi, ibn Hajar, as-Sakhawi, as-Suyuti and al-Albani.
It also appears in al-Hakim's al-Mustadrak -see here in Arabic with a commentary- and in at-Tabarani's al-Mo'jam al-Awasat -see here in Arabic- who commented saying that this hadith was only narrated via 'Abdullah ibn Wahb ابن وهب (the known Egyptian student of imam Malik). Ibn 'Ady counted three ways of the narration after ibn Wahb and ibn Hajar even corrected him showing that there are at least 6 people who heard it from ibn Wahb.
Note that the translation using "at the end" and "one who" is only an interpretation and does not go ahead with the meaning many scholars agree upon.
Interpretation of the hadith
The hadith by no means speaks about Awliya' Allah, but about scholars who do some kind of ijtihad to renew the religion for the people either by going back to the roots or with a new understanding/interpretation or showing off what went wrong during the last period or by pointing at things that people have committed, missed or not taken into account... so "renew" in the context might have a lot of meanings and the hadith by may be understood that every 100 years there will be scholars (not necessarily a single scholar) who may renew the religion.
More simply speaking it means Allah will send this ummah scholars or people of knowledge and guidance who will guide people back to the right path each time a majority of them might deviate.
Note that these people don't necessarily need to be the best of their time for example imam a-Shafi'i died at the beginning of the 3rd hijri century and was chosen as one of them although during the century he lived there where abu Hanfi, Malik, al-Laith and many great scholars ... also there is rarely a consensus on a single scholar.
In his commentary of Sunan abi Dawod called 'awn al-Ma'abood عون المعبود al-Aabadi محمد شمس الحق العظيم آبادي commented the hadith as follows -see here in Arabic-:
In the following I will translate from Arabic, as these are translations of my own take them with the necessary care!
( إن الله يبعث لهذه الأمة ) : أي أمة الإجابة ، ويحتمل : ( أمة الدعوة ) قاله القاري ( على رأس كل مائة سنة ) : أي انتهائه أو ابتدائه إذا قل العلم والسنة وكثر الجهل والبدعة . قاله القاري
(Allah will raise for this community) this refers to the ummah of al-Ijabah (Answer) (meaning the people who believe and follow the message of our prophet()) and it might refer to the ummah of ad-Da'awa (Call/Invitation) (meaning those people who have been invited to Islam by the prophet (): to mankind except with believing and practicing Muslims) this was an interpretation of (Mulla 'Ali) al-Qari. (at *the end' of every hundred years) means either at the beginning or end if the knowledge and the (practice of) sunnah decreased and the ignorance and innovation (bid'ah) rose this was said by al-Qari.
. وقال المناوي في مقدمة فتح القدير : واختلف في رأس المائة هل يعتبر من المولد النبوي أو البعثة أو الهجرة أو الوفاة ولو قيل بأقربية الثاني لم يبعد ، لكن صنيع السبكي وغيره مصرح بأن المراد الثالث انتهى
Al-Manawi in his introduction of Fath al-Qadir said: there was a difference of opinion on the meaning of ahead every hundred years whether the count should be starting with the birth of the prophet (), his mission (ba'atah), the hijrah or death and if it was said the second opinion seems close this wouldn't sound wrong, but as-Subki and others have declared the third as that what was meant End quote.
( من يجدد لها ) : أي لهذه الأمة ( دينها ) : أي يبين السنة من البدعة ويكثر العلم وينصر أهله ويكسر أهل البدعة ويذلهم .
(who will renovate) for this ummah (its religion) means by explaining and differing the sunnah from the bida'ah and by the rise of knowledge and the increase of students and scholars and the weakening of the people of innovation and their abasement.
Some of the scholars who have been considered as renewers
The scholars have a certain agreement that among these people were:
Two more detailed list appears in Arabic Wikipedia: see here and here which is the content of an Encyclopaedia on the renewers.
Some of my references the fatwas: on islamqa #153535 and islamweb #74655 (in Arabic language).
The Hadith you state can be found in Sunan Abi Dawud
Narrated Abu Hurayrah:
The Prophet (ﷺ) said: Allah will raise for this community at the end of every hundred years the one who will renovate its religion for it.
Abu Dawud said: 'Abd al-Rahman bin Shuriah al-Iskandarani has also transmitted this tradition, but he did not exceed Shrahil.
Sunan Abi Dawud
Of the Muftis and Imams I have asked this about, they have a general consensus that it signifies over a period of every 100 years Muslims will stray from the straight path. Many innovations (bidah) will enter the religion. Hence, Allah will sent someone who was brought up with the true understanding of the Quran and Sunnah.
This person will be a beacon for the people of the time.
You will have to elaborate on the term 'Wali ul Allah' because unfortunately many people have abused the term for their personal benefits. A true Wali ul Allah is someone who has submitted himself to God while remaining in this world and handling both deen & dunya. He/she is not after worldly possessions nor fame but works only for what is required to sustain himself and his family. Everything he/she does is for the pleasure of Allah and is based on the Quran & Sunnah.
There were a multitude of such people in the days gone and will be very few in the present and coming days.
Hadith Al-Bukhari:
On the authority of Abu Huraira who said: The Messenger of Allah (upon whom be Allah’s blessings and peace) said: “Allah the Almighty has said, ‘Whoever has mutual animosity with a friend (wali) of Mine, I declare war upon him. My servant does not draw near to Me with anything more beloved to Me than the religious duties that I have imposed upon him; and My servant continues to draw near to Me with supererogatory work such that I love him. And when I love him, I am his hearing with which he hears, his seeing with which he sees, his hand with which he strikes, and his leg with which he walks. Were he to ask of Me, I would surely give him; and were he to ask Me for refuge, I would surely grant him it.”
Another Answer Source:
“At the beginning of every century Allah will send to this ummah someone who will renew its
religious understanding.”
Narrated by Abu Dawood (4291);
classed as saheeh by as-Sakhkhaawi in al-Maqaasid al-Hasanah
(149) and by al-Albaani in as-Silsilah as-Saheehah (no. 599)