Just like e.g. Shopify, Big Commerce is a hosted or cloud e-commerce software, also known as Software as a Service (SaaS).
That means that the e-commerce provider, in this case, Big Commerce, host and maintain the e-commerce software for you. In return, you don’t need any traditional website hosting since it is all, i.e. hosting and software, delivered as one.
Generally, the benefits of this approach are:
After the initial set up, there is no need for you to have any technical knowledge or pay someone to maintain the software.
The downsides are usually considered to be the lack of access to the e-commerce software code, meaning it could be difficult to customize and integrate (other systems) with. In reality, SaaS providers address this objection by providing an apps marketplace, and an open API. These allow for extended functionality and the access needed to integrate any system.
On balance, SaaS is considered lower cost of ownership since there is no need to pay an additional cost to keep the software updated and hosted.