Nothing, but originally JILA was the Joint Institute for Laboratory Astrophysics. These days, that name doesn't begin to encompass the breadth of science conducted at JILA.
The name "Joint Institute for Laboratory Astrophysics" was chosen during JILA's planning stages in 1961 and 1962 while national interest in space science was very high. In response to the founding of NASA and the decision to put a man on the Moon, several government agencies were strengthening their space-related programs. NBS (National Bureau of Standards) was among these agencies, and it founded JILA jointly with CU (University of Colorado) as part of this effort.
However as JILA matured, its scientific interests moved significantly away from "laboratory astrophysics." Both the physics and astronomy communities lost interest in traditional laboratory astrophysics, and such research became difficult to finance. At the same time, JILA's astrophysicists were working theoretically more than experimentally. Lasers had become JILA's principal tool in experimental physics, providing more opportunities for atomic and molecular physics than for astrophysics.
After extended discussion in 1994, JILA's fellows decided to keep the word JILA but drop the meaning. The change was approved by CU and NIST (National Institute of Standards and Technology, formerly NBS) and became official in 1995.