Quotes from, The Politics of Military Coalitions By Scott Wolford, August 26, 2015.
"coalition members may contribute military forces directly, as the United Kingdom did during the 1991 Gulf War, as well as basing or staging rights, as did Turkey in the same war".
"Coalition members may contribute either military forces or territory for basing and staging support directly relevant to the threatened military action."
Staging, often used in the context of a staging area, refers to preparation.
In context of a military operation, it means preparing anything necessary for the operation, which could include troops, aircraft, any aspect of supply and logistics, etc, typically in the immediate vicinity both in time and space (as opposed to longer-term preparations that would be better described as "basing").
The US DoD definition is:
staging — Assembling, holding, and organizing arriving personnel, equipment, and sustaining materiel in preparation for onward movement. See also staging area. (JP 3-35)
The quoted passage is saying that Turkey provided bases and staging areas for other coalition members like the UK that are directly providing military forces.
