Afghan Arab or Arab Afghan is a term of convenience, first used for non-Afghan Muslim volunteers to fight the Soviets in the Afghanistan War (1978-1992). While the first such volunteers were indeed primarily Arab, they later came to include Chechens, Sudanese, people from Southeast Asia, and Western converts. After the Soviets left, the term also came to include non-Afghan jihadists operating from Afghanistan and sometimes Pakistan.
Ethnic Arabs are not native to Afghanistan, and, while many Muslim Afghans speak the Arabic language, it is not a native language.
While the first such volunteers were spontaneous, often traveling on their own, various organizations, such as the Services Office, facilitated their travel, usually through Pakistan and with the knowledge of Pakistani Inter-Services Intelligence. Abdullah Azzam and Osama bin Laden were involved in the Services Office.
Many of the "Afghan Arabs" had cultural and theological differences from the native Afghans. While Afghans are legendary fierce fighters, deliberate martyrdom and suicide attack was not within their traditions, while some of the volunteers courted death.
It was U.S. Cold War policy to encourage anything that would harass the Soviets in Afghanistan, but there was very little direct involvement in Afghanistan proper; ISI received funding from the Central Intelligence Agency to support these operations. There was also cooperation between ISI and the Saudi General Intelligence Department, under the direction of Prince Turki al-Faisal. al-Khifa, in the U.S., probably did receive direct funding.
Since the 9-11 attack hijackers were funded through Afghanistan and Pakistan and received some training there, they fall into the general category of "Afghan Arab" although they were primarily Saudi, recruited in Germany and elsewhere, and operating in the U.S. In the Afghanistan War (2001-), some of the most fanatical "Afghan Arab" fighters were actually Chechens.