bash can be started in interactive mode or non-interactive mode. It can also act as a login shell or a non-login shell.

bash is started in interactive mode by your terminal emulator and can also be started in interactive mode like this:

bash
bash -i
bash -ic 'echo Hello!'

When you run a script through bash or if you start it with the -c option, it will run in non-interactive mode:

bash script.sh
bash -c 'echo Hello!'

bash is instructed to act as a login shell when you first log in to your machine or when you start bash with the --login or -l option.

.bashrc is sourced on every start in interactive mode when bash does not act as a login shell.

.bash_profile is only sourced when bash is started as an interactive login shell, or as a non-interactive shell with the --login option.

This means that .bash_profile is great for commands that should run only once and .bashrc for commands that should run every time you start a new shell.

For example, PATH customization should only happen once, since it is not an idempotent operation. Suppose something like this was in your .bashrc:

export PATH="$PATH:/addition"

Running these commands from a newly started interactive shell would produce the output below:

bash
bash
echo "$PATH"
/original_path:/addition:/addition:/addition

Setting PATH in .bash_profile alleviates this problem.