Easy Redmine is an Open Source software. It is licensed under GNU GPL 2 as stated here. By buying the software you obtain an installable package and the source code.
Server solution versus Cloud - how do these 2 work?
Server solution
The server solution is designed for your own server (you host the software). By purchasing this solution you obtain installable software + the source code.
The cloud solution is hosted on servers of Easy Software Ltd. in various locations. Easy Redmine Cloud has 10 geolocations right now and more are coming soon. Please check the map of Easy Redmine cloud here. By purchasing this solution you obtain the right to use the software in the cloud for a defined period of time.
The cloud solution includes software updates for the whole hosted period.