E-commerce platforms are software tools you can use to implement an e-commerce site, without having to design it from scratch yourself. These are sometimes called turnkey solutions, because instead of building it yourself, you just "turn the key" and get started immediately.
Magento is a widely used e-commerce platform. A very simple example of a site implemented with Magento is Quay Performance Sailing.
Amazon's e-commerce platform is called Webstore.
Shopify is yet another e-commerce platform. See how easy this is?