Solutions are for Application Lifecycle Management (ALM).
Imagine you have a client that wants to play around on an app with demo data in order to give feedback on the changes she wants before her staff starts using it. You would build the app in a Solution inside a Sandbox environment, work with her on developing it and get it to it's ready-for-production state.
Now that it's ready for production, you take the solution, which is a bundle of all the app components, and export it out of your Sandbox environment and import it into the production environment. None of that demo data comes with it, and the staff has an app they can use.
Over the next few months, your client has some ideas she wants to try out, so you build those in a solution in the Sandbox environment, while the staff continues to use the production version. When the changes are ready, you export the new solution version, import it into production environment, and there is no production downtime to develop the new app version.
I hope that clears it up a little.
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