'Abd al-Qadir
It is his personal name, meaning "Servant [or Slave] of the All-Powerful." (The form 'Abdul Qadir, which the reader may come across elsewhere, is simply an alternative transliteration of the Arabic spelling)  It has always been a common practice, in the Muslim community, to give a male child a name in which 'Abd is prefixed to one of the Names of Allah.
Al-Jilani
A surname ending in -ii will often indicate the bearer's place of birth.  Sheikh 'Abdul Qadir was born in the Iranian district of Giilan, south of the Caspian Sea, in A.H. 471/1077-8 C.E.  (In some texts, the Persian spelling Giilanii  is used instead of the arabicized form al-Jiilaanii.  The abbreviated form al-Jiilii, which may also be encountered, should not be confused with the surname of the venerable 'Abdul -Karim al-Jiilii, author of the celebrated work al-Insan al-Kamil, who came from Jiil in the district of Baghdad).
Let us now consider a slightly longer version of the Sheikh’s name, as it occurs near the beginning of Al-Fath ar-Rabbaanii [The Sublime Revelation]:  Sayyidunaa 'ash-Shaikh Muhyi'd-Diin Abu Muhammad 'Abdul-Qadir (Radiya'llaahu 'anh).
Sayyidunaa 'ash-Shaikh -
"Our Master, the Sheikh."  A writer who regards himself as a Qadirii, a devoted follower of Sheikh 'Abdul -Qadir, will generally refer to the latter as Sayyidunaa [our Master], or Sayyidii [my Master].
Muhyi'd-Diin
"Reviver of the Religion".  It is widely acknowledged by historians, non-Muslim as well as Muslim, that Sheikh 'Abdul-Qadir displayed great courage in reaffirming the traditional teachings of Islam, in an era when sectarianism was rife, and when materialistic and rationalistic tendencies were predominant in all sections of society. In matters of Islamic jurisprudence [fiqh] and theology [kalam], he adhered quite strictly to the highly "orthodox" school of Imam Ahmad ibn Hanbal.
Abu Muhammad
"Father of Muhammad".  In the Arabic system of nomenclature, a man's surnames usually include the name of his first-born son, with the prefix Abu [Father of–].
Radiya'llaahu 'anhu
"May Allah be well pleased with him!"  This benediction is the one customarily pronounced–and spelled out–in writing after mentioning the name of a Companion of the Prophet (Allah bless him and give him peace).  The preference for this particular invocation is yet another mark of the extraordinary status held by Sheikh 'Abdul-Qadir in the eyes of his devoted followers.
Finally, we must note some important elements contained within this even longer version:  al-Ghawth al-A'zam Sultan al-Awliyaa' Sayyidunaa 'ash-Shaikh Muhyi'd-Diin 'Abdul-Qadir al-Jiilanii al-Hasanii al-Husainii (Radiya'llaahu 'anh).
Al-Ghawth al-A'zam
"The Supreme Helper" (or, "The Mightiest Succor"). Ghawth is an Arabic word meaning:  (1) A cry for aid or succor.(2) Aid, help, succor; deliverance from adversity.(3) The chief of the Saints, who is empowered by Allah to bring succor to suffering humanity, in response to His creatures' cry for help in times of  extreme adversity.
Sultan al-Awliyaa
"The Sultan of the Saints".  This reinforces the preceding title, emphasizing the supremacy of the
Ghawth above all other orders of sanctity.
al-Hasanii al-Husaini
"The descendant of both al-Hasan and al-Husain, the grandsons of the Prophet (Allah bless him and give him peace)." To quote the Turkish author, Sheikh Muzaffer Ozak Efendi (may Allah bestow His mercy upon him):  "The lineage of Sheikh 'Abdul-Qadir is known as the Chain of Gold, since both his parents were descendants of the Messenger (Allah bless him and give him peace).  His noble father, ‘Abdullah traced his descent by way of Imam Hasan, while his revered mother, Umm al-Khair, traced hers through Imam Husain".