Schumann resonances occur because the space between the surface of the Earth and the conductive ionosphere acts as a closed waveguide. The limited dimensions of the Earth cause this waveguide to act as a resonant cavity for electromagnetic waves in the extremely low frequency band. The cavity is naturally excited by electric currents in lightning.

Resonant frequencies abound in nature. The atoms in your body are basically extremely small structures vibrating at specific frequencies. The Schumann resonance is not special in this regard.

The first video, like most assertions of its kind, mixes factual information with unsubstantiated claims. For example, the narrator of the video states that the Schumann frequencies are always present (true), are created by lightning (also true), and mimic human brainwaves (demonstrably false -- human brainwaves contain a range of frequencies, not just the Schumann one). He then concludes that Schumann frequencies must be critical to life itself, just as food and water is (an unsubstantiated claim, not supported by the facts).

Two of the "facts" mentioned in the video that can easily be disproven:

1. Astronauts returning to Earth are weak because they have been deprived of the Schumann frequencies by being in outer space (The real reason is that we evolved in Earth's gravity, and become weak when we are deprived of it), and

2. Because of this, NASA created devices that mimic the Schumann resonance on the space shuttle (never happened).

Just because an explanation is plausible doesn't mean it is true.