The Subdivision Surface Modifier is used to split the faces of a mesh into smaller faces giving a smooth appearance. Using this modifier, enables you to model complex smooth surfaces with simple, low-vertex meshes. This allows modeling of high resolution meshes without the need to save and maintain huge amounts of data and it gives a smooth organic look to the object.

This process creates virtual geometry that is generated non-destructively without modifying the original mesh, but it can be converted to real geometry that you could edit with the Apply button.

More on the Subdivision Surface modifier at the Blender Manual