Instantaneous luminosity measures how tightly particles are packed into a given space, such as the LHC's proton beam. A higher luminosity means a greater likelihood particles will collide and result in a desired interaction. This can be achieved by packing more particles in the beam, or by focusing the beam more tightly.
Integrated luminosity, on the other hand, considers the total number of events during a period of data-taking. The ATLAS Experiment recorded 147 inverse femtobarns of data during the LHC's 13 TeV run from 2015-2018, which equates to about 16 million billion proton–proton collisions!
Check out the cross section and luminosity cheat sheet to learn more.