When an operating system works with a local drive, the operating system uses filesystem software to format the drive, and then read and write individual sectors. When you save a file, the filesystem software figures out the sectors to write to. When you read a file, the filesystem figures out which sectors the data is on, and then reads those sectors and reconstructs the file for you.
To manage the files, the filesystem uses different types of indexes that it also stores on the disk. Different filesystems use different means to organize the data, and also include various security mechanisms; the end result is different file systems such as ext4 and NTFS.