Restore database in SQL Server 2005

BACKUP DATABASE [MPRM] TO  DISK = N'\\rauf\shared\MPRM_15_5_10.BAK' 
WITH NOFORMAT, NOINIT,  NAME = N'MPRM-Full Database Backup', 
SKIP, NOREWIND, NOUNLOAD,  STATS = 10

The backup process worked, and I got a file named MPRM_15_5_10.BAK in my shared folder (D:\shared\). This is a backup created from another machine.

When I try to restore the backup, using the following script

RESTORE DATABASE [MPRM] 
FROM DISK = N'\\rauf\shared\MPRM_15_5_10.BAK' 
WITH FILE = 1,  NOUNLOAD, STATS = 10

I get the following errors

Msg 5133, Level 16, State 1, Line 1
Directory lookup for the file "E:\DATABASES\MPRM.mdf" failed with the operating system error 2(The system cannot find the file specified.).
Msg 3156, Level 16, State 3, Line 1
File 'MPRM' cannot be restored to 'E:\DATABASES\MPRM.mdf'. Use WITH MOVE to identify a valid location for the file.
Msg 5133, Level 16, State 1, Line 1
Directory lookup for the file "E:\DATABASES\MPRM_log.ldf" failed with the operating system error 2(The system cannot find the file specified.).
Msg 3156, Level 16, State 3, Line 1
File 'MPRM_log' cannot be restored to 'E:\DATABASES\MPRM_log.ldf'. Use WITH MOVE to identify a valid location for the file.
Msg 3119, Level 16, State 1, Line 1
Problems were identified while planning for the RESTORE statement. Previous messages provide details.
Msg 3013, Level 16, State 1, Line 1
RESTORE DATABASE is terminating abnormally.

Why the system asks about *.mdf, *.ldf files ? Is it anything related with Backup option rather than Restore script ?

I logged in with Windows Authentication

You need to specify where to store the physical files when you restore a .bak if your target server doesn't have the same disk/directory layout as the original source server. The backup file contains the logical SQL Server files along with the original location on the source server (the full physical path where the .mdf and .ldf where located).

So you need to use something like this:

RESTORE DATABASE [MPRM] 
FROM DISK = N'\\rauf\shared\MPRM_15_5_10.BAK' 
WITH FILE = 1,  
MOVE N'MPRM' TO N'D:\MSSQL\Data\MPRM.mdf',  
MOVE N'MPRM_Log' TO N'D:\MSSQL\Data\MPRM_Log.ldf',  
NOUNLOAD, REPLACE,  
STATS = 10

This command here:

MOVE N'MPRM' TO N'D:\MSSQL\Data\MPRM.mdf',

specifies that the logical file called MPRM (that's the default when you didn't specify anything else when creating your SQL Server database) should be moved during restore to the physical location D:\MSSQL\Data\MPRM.mdf (adapt this as needed)

To just see what is contained inside a backup file, you can use this command here:

RESTORE FILELISTONLY
FROM DISK = N'\\rauf\shared\MPRM_15_5_10.BAK'

This will show you all the logical files inside your backup, along with their original physical file that they were backed up from (on the source server, where you ran the backup command).