Such question became viral to the general public after some security researchers pointed out this on a DEF CON presentation about their walkthrough on a Boeing 747. This shouldn’t be a novelty for someone working closely to airline operations and maintenance, but certainly kind of surprising for anyone else.
An airplane relies on different sort of systems, and modern aircraft have many electronic controls which can be updated with time due to different reasons and needs. Just to mention a few of software updates possible in aircraft systems, there is the engine control system and the flight management system (which includes aircraft performance data and navigation database).
Since most aircraft flying out there have been designed in the 1980’s or early 1990’s when floppy disks were the “state of the art” technology, their use is mainly as a remnant of old times: the process to make such design changes in aircraft systems is really expensive (due to certification), as it involves many safety and security aspects.
However, as you look for newer aircraft models, that legacy technology may be substituted for newer ones: a good example of that is the A320, with its original project from the 1980’s (known as A320ceo, and which uses floppy disks), while his new version, the A320neo, from 2010’s, has “retired” the floppy disks.
As older aircraft models reach the end of their life-cycle, we might finally get rid of the floppy disks, but maybe still see the manual process of updating there, due to cybersecurity and reliability.