Before the revamp of the ADF Dedicant Path, the original requirement was for meditation specifically, rather than for the broader concept of mental discipline that replaced it.
I'm actually glad that I did that requirement under the old rules, as I might not have discovered meditation at all otherwise.
My partner, Steve, spent seven years in a Japanese monastery, and he's the one who taught me how to sit. While Zen meditation techniques are not Indo-European, necessarily1, they do work, and have given me not only mental discipline, but also a sense of calm in the midst of everyday dramas.
Meditation, as I understand and practice it, is an extremely focused practice, where the mind is concentrated on a single experience, idea or chant, with the avowed purpose of forcing the ego to retreat and allow one to exist for a time totally in the present, in a state of conscious silence. Here, internal stimuli are reduced and the external ones increased.
When I first started meditating, I found it to be incredibly difficult. Steve showed me how to sit, and told me to do just what the old DP handbook said, to count my breaths with my eyes open. He had me look down at an imaginary spot somewhere in front of where I was sitting, and loosely stare at it in an unfocused way.
For each sitting, I would count a full breath, in and out, as one breath. I would take nine breaths as a single cycle, and I would repeat this cycle nine times, for a total of 81 breaths. I kept count by gently lifting a finger for each cycle. In time, I finally got to the point where I'd only have to breath five or six times before I could abandon all that counting.
But as a beginner, I needed that counting badly. My conscious mind rebelled at my insistance that it quiet down, as my ego hated the idea of losing control. Counting the breaths was something that I could hang on to, at least.
But thoughts still intruded. Indeed, they didn't go away at all for weeks! But someone told me to think of meditating as sitting before a swiftly flowing river, and to think of my thoughts as leaves floating on that river. I had a choice - I could pick up one of those leaves (thoughts) and hold it up to my face and examine it, or I could just let it float on down the river. In other words, whenever thoughts would intrude, I had the choice of grabbing a hold of them, and thinking about them, or I could see the thoughts and let them go, neither holding on nor suppressing them. This worked in time. Now I can go for whole minutes without thoughts intruding!
So Why Bother?
According to the website of the University of North Dakota, scientific evidence is accumulating that suggests that meditation does indeed induce changes in the brain caused by the simple act of focusing. While there is much work to be done, it is apparent that something's going on.
Learning to meditate has given me a bit of control over my mind, and this has enabled me to trance better, visualize better, and (I hope) do better magic. I know that the stillness that meditation can give me has made me a better priest. So this is the form of mental discipline that I practice. And I recommend it highly.
1Steve tells me that he was taught in Japan that Zen meditation was descended from practices originating in the Indus Valley civilization that were adopted by the conquering Vedics. From there they passed into Hinduism and Bhuddism. All cultures borrow from their neighbors.