OpenSubdiv is an open-source subdivision method developed by Pixar that lets you work with a high-fidelity representation of your model. As a professional standard in the animation industry, OpenSubdiv is implemented in a variety of software packages, improving interoperability by producing the same results when models are transferred between applications. In Maya, OpenSubdiv is the default subdivision method when you preview a smoothed mesh, or smooth a mesh using Mesh > Smooth.
OpenSubdiv is an improved alternative to the legacy Maya Catmull-Clark subdivision method. For example, OpenSubidv takes advantage of parallel GPU and CPU structures, improving viewport performance for meshes with high subdivision levels. Additionally, you can turn on Show Displacements in the OpenSubdiv Catmull-Clark Controls to visualize displacement maps interactively without the need to render.
OpenSubdiv Catmull-Clark Adaptive: Applies a progressive refinement scheme to irregular parts of your mesh. Adaptive subdivision only refines the mesh topology where additional detail is needed. It uses the GPU to generate a high resolution mesh that can be rendered at a high frame rate, without affecting your scene's performance. Adaptive subdivision supports high levels of tessellation and adjusts tessellation based on camera position, providing you with a smooth mesh whether your model is close to the camera or far away.