The storage emulator listens at the address you see there, but when requests come in it uses the SQL store as the back end storage.
The storage emulator uses SQL Server LocalDB by default, or you can use the DSInit.exe command line utility to point it at a full SQL Server instance. All table, queue and BLOB data is then saved in that database. In the case of BLOBs the metadata is stored in the database, but then the file is stored in an appdata directory. For example, one of mine was in c:\users\michael\appdata\local\developmentstorage\sql\blockblobroot\1\c1ba3640-ad8e-4cbb-8818-95c7d866cb71.
If you point your emulator at a SQL Express or SQL Server instance you can then use SQL Management Studio to connect to that instance and dig into the tables. There is a table named Blob with a column of DirectoryPath which will tell you were the files are. I wouldn't go messing around much with the structure of this database, or the file structure outside of using the API or a storage tool or you may cause issues with your local emulator stability.
Also note that this is NOT how the data is stored in Windows Azure, only how the local emulator simulates it.