Basically I\'ve followed a tutorial and decided to delete the .mdf file afterwards.
Now whenever I try to run the application I get the following error
You already have an old copy of that database installed in Server Explorer. So its a simple naming collision in the Server Object Explorer / SQL server. You likely created the same database Catalog Name already before you decided to move it to the Apps_Data folder. So that Database name already exists and just needs to be deleted.
Just go into Visual Studio > View > SQL Server Object Explorer and delete the old database name and its connection. Retry your app again and it should install the .mdf file in App_Data and create the same exact database again in the Server Explorer.