Hi Anastasia,
you described a classical vipassana meditation, which calms the mind.
Collins dictionary provides a rather western idea of meditation, relating it to contemplation. Which it usually is not in the East.
And Vipassana is but one kind of meditation, there a so many others that the term itself is used more like a general idea of a number of methods of working with mind in kind of a "spiritual" way.
Whatever that is.
It is actually not a complicated process. The complicated part is calming our constant stream of thought-babbling.
Before starting to meditate, it might be a good idea to ask oneself about the goal.
Becoming more stable (Vipassana, Mindfulnessbased stress reduction)? Performing better and earning more money (certain cults)? Become ultraspiritual (Guru Wishywashy)? Controlling body, mind and even the circumstances by gaining power (some Hindu meditations), seeking enlightenment no matter what it takes?
All of them have their pros and cons.
Do I only want the method and stay away from the philosophical / religious background? Do I want to get involved with other practitioners or rather practice alone (some actually manage)?
Goals and preferences may change.
But it seems a good idea to check them every once in a while.
The other day, I attended a Buddhist congress. Lots of different schools and traditions. They were amazingly different. As always, I tremendously enjoyed meeting Zen practitioners, people from different Vajrayana (Tibetan Buddhism) schools, Mahayana traditions and some Theravadins. Nice family gathering. And much alike a family clan, some groups relate closer than others.
Wildly different, both terms of methods and of the kind of people, they attract. And that was only Buddhism.