> isn’t our whole life a sequence of meditations? Because we always focus on something
Focus is only the method (one of many), not the goal. In (eg) vipassana meditation, the goal is "to see things as they really are."
> meditation is “doing nothing”. Okay, but then again there’s nothing special about it, we all do it from time to time.
Meditation is not "doing nothing," it's actually a very active process. If anything it's more like the practice of intentionally thinking nothing. This is not as easy as it sounds.
One of the early meditation exercises is to sit quietly and count to ten slowly (perhaps one count for each breath, and each breath taking a ~5 second inhale, ~7 second exhale). When you notice your mind drift to something else, refocus on the counting and start over at zero. The goal is not really to reach ten (if you do, start over at zero). The purpose of the exercise is to realize how noisy our internal thoughts and feelings are, to practice observing them, letting them go, and refocusing on your focal point (counting or breath, etc).
There's nothing special about running, we might find ourselves doing it from time to time. But then why do people jog? Meditation is similar. It's an exercise.
And to further emphasize doing vs thinking: meditation has very little to do with what we're physically doing. You can meditate while walking, driving, or doing any activity. (It's just harder to do because there are more distractions.)
> just sit peacefully and observe your thoughts. Then again, aren’t we doing it anyway on a regular basis without introducing a word for it?
We are not, typically, observing our own thoughts. We're thinking thoughts, and feeling our feelings, but not actively observing them. But meditation is not just observing thoughts, but also letting them go without attaching to them. Letting every seed of a thought float away without taking root.
> Can you please share your own personal specific definition — what exactly is a meditation for you?
Meditation (to me) is the practice of letting go of thoughts. By doing this enough times, we strengthen the process so it becomes automatic. The goal is so we can observe our own thoughts and feelings, and everything around us, from a more calm and clear point of view. "To see things as they really are." It also has other benefits.
To be concrete: after waking up I set a timer (anywhere from 1-40 minutes depending on what I need) and sit quietly with my eyes closed (or sometimes open). I focus on my breath and all the sensations around me: the sound of the fan, the tension and release of muscles, etc. When a thought pops up, I let it pass by without judgment or attachment and return my focus to my breath. When the timer goes off, I'll continue meditating for a few minutes if my mind is really restless.
After meditating I'm typically in a calm, collected state, ready to start my day. Throughout the day, when I remember, I'll return to that state of awareness (of everything inside and around me) and meditate for a few moments during whatever I'm doing. After meditating regularly for a few months, I find this process will happen throughout the day without forethought (just automatically out of nowhere). When something happens that triggers an emotional reaction in me, I'll see the emotion as though it's a button I could choose to press or not.
I know you don't like analogies, but meditation is like you're following a toddler walking down a path. The toddler wanders every which way, following whatever whims. Each time it leaves the path, you gently and without judgement pick it up and return it to the path. It doesn't matter how many times you do this, the toddler will always leave the path. The goal is not to teach the toddler to stay on the path. The goal is not to keep the toddler on the path. The goal is to strengthen your arms so you can return the toddler without effort. This is the practice of meditation.