What is the difference between Visualforce page and lightning component?

Visualforce follows a Page-Centric model. PageCentric means that the goal of Visualforce is to create something that is your full-page interface. When the user has to perform some operation, eg Create a record or save a record, it sends that request to the Salesforce servers and then reloads the entire page with the new state of the UI. All backend processing is done with Apex Code on the Server-Side.
Lighting Component is an App-centric approach. Lightning components are part of the Salesforce user interface framework for developing dynamic web applications for desktop and mobile devices. They use JavaScript at the client-side and Apex at the server-side to provide the data and business logic.