There are a number of benefits to tessellations:
1. We can implement a level-of-detail (LOD) mechanism, where triangles near the camera are tessellated to add more detail, and triangles far away from the camera are not tessellated. In this way, we only use more triangles where the extra detail will be noticed.
2. We keep a simpler low-poly mesh (low-poly means low triangle count) in memory, and add the extra triangles on the fly, thus saving memory.
3. We do operations like animation and physics on a simpler low-poly mesh, and only use the tessellated high-poly mesh for rendering.