The Linux filesystem is structured in a specific way. Essential binaries are in
/bin/, boot loader files are in
/boot/, most device files are in
/dev/, mount points for removable media are in
Some minor details may differ from distro to distro (e.g.
/usr/local/bin/), but in general almost all Linux distros follow the same directory structure.
To answer your question:
The users' home directories are in
/home/. In principle, Linux is a multi user operating system. You may just have one user account on your laptop with its home directory in
/home/<username>/, but if you look into
/home/ on a shared Linux server, you will see many home directories: one for each user account. The idea is that every user of the system has write permissions only in their own home directory. If your username is
bob you can read and write and delete files in
/home/bob/ but you cannot touch anything in
/home/alice/ or in
root is different though.
root is the administrative user and has write privileges everywhere on the system (and can act as any user of the system). So it makes sense that
root has the special home directory
root is not a regular user. Other than that,
/root/ is just a regular directory with no special magic, although it is quiet possible (even likely) that system utilities rely on
/root/ being the home of user
When you execute
sudo -i in a terminal, you switch from being e.g. the regular user
bob to being
root. Note that this switch affects only the terminal window where you typed
sudo -i. For your file manager you are still
bob and if you open another terminal window you are still
bob in there. In this context the symbol
~ is a shorthand for the current user's home directory. For
/home/bob/ but for
I hope that clarifies things for you.