The study monitored brain waves through the use of EEG (electroencephalography). Electrodes were placed in standard locations of the scalp using this custom-made hat.

This study found that nondirective meditation causes brain wave activity that’s associated with more wakeful, relaxed attention than just resting.

Increased Theta and Alpha EEG Activity During Nondirective Meditation, The Journal of Alternative and Complementary Medicine, November 2009

Brain Waves And Meditation, Science Daily, March 2010

There are many styles of meditation. The kind I learned years ago might be considered mindfulness or nondirective meditation, where you become an observer of your thoughts. When you have a thought, because you are going to!, you don’t latch on to it or keep thinking it. You recognize that you’re having it, then you move back to the breath. When you do this, gently, over and over and over again, you come to appreciate that we are not our thoughts.*

This study found that nondirective meditation stimulates certain brain waves that cause us to feel more refreshed.

What this meditation is not:

Meditation research explores how the brain works when we refrain from concentration, rumination and intentional thinking.

Meditation is not the same as resting:

[Participants] were asked to rest, eyes closed, for 20 minutes, and to meditate for another 20 minutes, in random order.
…
During meditation, theta waves were most abundant in the frontal and middle parts of the brain. “These types of waves likely originate from a relaxed attention that monitors our inner experiences. Here lies a significant difference between meditation and relaxing without any specific technique,” emphasizes [principle investigator] Lagopoulos.
…
Alpha waves were more abundant in the posterior parts of the brain during meditation than during simple relaxation. They are characteristic of wakeful rest.

Meditation is not the same as sleeping:

Delta waves are characteristic of sleep. There was little delta during the relaxing and meditative tasks, confirming that nondirective meditation is different from sleep.

What nondirective meditation is:

Several studies indicate better relaxation and stress management by meditation techniques where you refrain from trying to control the content of the mind. … “These methods are often described as nondirective, because practitioners do not actively pursue a particular experience or state of mind. They cultivate the ability to tolerate the spontaneous wandering of the mind without getting too much involved. Instead of concentrating on getting away from stressful thought and emotions, you simple let them pass in an effortless way.”

* “… you come to appreciate that we are not our thoughts.”

Here’s Jon Kabat Zinn, whose work we studied back then. Notice what he says about selfing.