One of the main Islamic organizations which seek to establish an Islamic domination of the world and do not hesitate to use acts of terror for this goal. Al-Qaeda is headed by Osama bin Laden and became best known for the terror attacks on the World Trade Center on September 11th, 2001.
Further reading: Islam & Terrorism
The word Qaeda meaning "Base" or "Foundation" is a noun derived from the verb Qa'ada (to sit) and is used like in the following examples:
Military Use:
Military Base,
Operational Base,
Air Base,
Navy Base
Construction: The foundation
Political: The population or the masses behind a movement.
The inference here appears to be: the essential building block and the foundational source of the Islamic movement. It implies or presumes a strong support at the grassroots level. The claim is that they are the real true representatives of the Islamic movement.