The room does the pushing
Why Does Suction Pick Things Up?
A vacuum throws air out of itself, so the room's air pressure pushes dust in to fill the gap.
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Step 1 of 5
Suction is a push, not a pull.
Air cannot reach out and grab anything. Everything that looks like suction is really the surrounding air pressing inward on its own.
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Step 2 of 5
A spinning fan throws air out.
Curved blades fling air outward and out of the machine's exhaust, and that air does not come back in through the hose.
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Step 3 of 5
That leaves fewer air molecules inside.
With air being removed faster than it returns, the pressure in the hose falls below the pressure everywhere else in the room. Even with the nozzle blocked, that is a drop of about a fifth.
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Step 4 of 5
Air rushes to even it out, dragging dust.
Pressure differences never last. Room air pours into the low-pressure hose, and anything light enough gets swept along in the current.
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Step 5 of 5
The dust has to be separated out again.
Air and dust are spun round a tight bend so the heavier grit is flung to the outside wall and drops away, letting cleaner air reach the fan.
A household vacuum lowers the pressure in its hose by only about a fifth, which is why it cannot lift anything very heavy.
The short version
Nothing sucks — the fan throws air out of the exhaust, the hose drops about a fifth below room pressure, and the room pours back in dragging dust with it. A tight bend inside then flings the grit clear.
Try it yourself
Hold your palm flat over the hose. The motor note rises and the machine strains, because no air can rush in for the fan to move.