Think of it like this. A graphics card contains it's own processors, RAM, etc that are specifically designed to handle data relative to graphics, whether that be polygon geometry, textures (images), pre/post-processing effects, etc. Whatever can be rendered (which is a term for processing a model/scene into an image that gets displayed) by the graphics card is sent to it, held in its RAM, and processed there instead of through the CPU (so long as the graphics card has the capability).
Hardware tessellation can be defined as a process of increasing the complexity of a polygonal model without having to manually add that complexity in.
Here's a visual representation of hardware tessellation...