Dataplicity is a new service that aims to simplify the process of connecting to your devices over the internet. As with many services there is a free account which allows you to try it out with paid accounts for commercial or heavy users. Once configured the service gives you access to your command line terminal from anywhere on the internet via desktop or mobile devices.
The concept behind Dataplicity is to simplify the process of making your Pi available over the internet. Previously you had to deal with IP addresses and router port forwarding. This was hard for some people to manage as the process varied depending on their ISP and router setup.