They speak in term of raw energy, carried by the photons the sun sends us. If we had 100% efficient solar panels and covered the entire earth with them we'd get 173,000 terrawatts of electrical power.
Yeah it should be per second. If you run the numbers that's the solar power falling on the Earth. But to capture it you need to be above the atmosphere, only about 75% reaches the Earth's surface.
But Dyson had this great spherical concept, so maybe there is a way to get a lot of that energy while still, like, living on the planet.