PhysX is an open-source realtime physics engine middleware SDK developed by Nvidia as part of the Nvidia GameWorks software suite.
Initially, video games supporting PhysX were meant to be accelerated by PhysX PPU (expansion cards designed by Ageia). However, after Ageia's acquisition by Nvidia, dedicated PhysX cards have been discontinued in favor of the API being run on CUDA-enabled GeForce GPUs. In both cases, hardware acceleration allowed for the offloading of physics calculations from the CPU, allowing it to perform other tasks instead.
PhysX and other middleware physics engines are used in many video games today because they allow game developers to save development time by not having to write their own code that implements classical mechanics (Newtonian physics). To do, for example, soft body dynamics.