Symmetry lets you reflect detail from one side of a polygonal model to the opposite side. 
Symmetry in Maya is selection-based. When symmetry is turned on, the selected component(s) and the component(s) on the opposite side of the mesh are included in the selection, letting you perform selection-based polygonal modeling operations with symmetry.
Topological symmetry
If your model is topologically symmetrical but is posed in an asymmetrical manner or contains vertices that overlap in 3D space, you can still edit your mesh using topological symmetry. Unlike the other symmetry modes (World and Object), which rely on 3D space to determine points of symmetry, topological symmetry uses the model's topology to find symmetrical components. See Edit a mesh with topological symmetry.