The experimenters set up a system that could detect slow-wave (SW) fluctuations in brain activity. They used trans-cranial magnetic stimulation (electro-magnets on the scalp) to "augment" this SW activity. This seems to have improved memory, measured by some specific learning task they set for the participants.
Trans-cranial magnetic stimulation is becoming popular in trans-human type circles. Apparently it's becoming feasible to do at home with cheap off the shelf components. However, of course, the long term effects and side effects are poorly understood.
This particular experiment used 16 participants (only three of whom were female, for some daft reason) so we can't draw any firm conclusions from this.
From Wikipedia: "ECT is often used with informed consent as a last line of intervention for major depressive disorder, mania, and catatonia. ECT machines have been placed in the Class II category (special controls) by the United States Food and Drug Administration (FDA) since 1976." (Emphasis mine.)
I don't think we are close to understanding the brain either.