When exactly to use php bin/magento setup:upgrade

If you enabled one or more modules, then you will need to run magento setup:upgrade to update the database schema.

By default, magento setup:upgrade clears compiled code and the cache. Typically, you use magento setup:upgrade to update components and each component can require different compiled classes.

magento setup:upgrade --keep-generated

The optional --keep-generated option should be used only in limited circumstances by experienced system integrators. --keep-generated should never be used in a development environment.

Improper use of this optional parameter can cause errors during code execution.

UPDATE (07/10/17)

As the topic creator asked me:

But its just so strange for me, because everytime I'm doing some changes, they won't be visible until after I run the setup:upgrade command. Even if I delete the var/cache, its still not visible. Do you know any reason for this?

var/cache in Magento 2 is not enough to makes changes visible like Magento 1. In Magento 2, you will need to clears var/generation (and var/di if you compiled code) after you made changes inside your code, especially whenever you change something inside the constructor.

You will also need to clear var/view_preprocessed if you change something inside your template file (.phtml)

The rest will goes to var/cache and var/full_page_cache

Hope this helps.