I am a little bit confused about /proc directory. Each process frequently updating its state, memory info, progress etc in their process.
My question is that the /proc directory keeps the memory or writes on harddrive each information.
What I believe that It frequently updating the information it takes IO operations and it no further uses when computer restart so it might be in the memory.
The /proc directory itself exists as an empty directory on the hard drive. It's contents, however, are added by the kernel without touching the disk. If you try to access /proc before it is mounted (say, booting your system with nothing but a shell with init=/bin/sh), it will be empty.
You can replicate /proc on any directory with mount -t proc proc /path/to/directory.
Just like ext4, fat32, etc., proc is a filesystems. (It is referred to as a pseudo filesystem because it cannot actually be used for storing files. If you try to do so, even as root, it will not work.) There are 'real' filesystems like proc that don't write to the disk, say ramfs/tmpfs. These filesystems don't actually write their files the disk, rather keeping them in the system ram. (If it isn't already there, I recommend adding the line tmpfs /tmp tmpfs rw 0 0 to your /etc/fstab so that temporary files written to /tmp don't actually get written to your disk.)
There are a few other pseudo filesystems, like sysfs on /sys and devtmpfs on /dev. (/dev is slightly different. It isn't maintained by the kernel, and devtmpfs isn't always mounted over /dev, sometimes block files are written directory to the disk.)
