Not sure if it was my comment https://news.ycombinator.com/item?id=47907337 which does have a video like that. But, the Brompton folding design:

- folds in 3 pieces (tri-fold) instead of folding in half (bi-fold). It was innovative at the time, is more common now. That makes it fold smaller than bi-fold bikes.

- keeps the oily chain and chainrings in between the wheels. Some other bikes which only fold in half have the oily bits on the outside[1], and/or the chainring sticking quite far out[2]

- When folded, the mucky main wheels are lifted off the ground by the little roller wheels[3].

- Brompton folds into almost a square which can stand up on its own, or pack reasonably neatly into a box, bag, or trunk. Other bikes can be more pointy, less convenient shapes when folded. e.g. [1] the bar grips stick out, the pedal sticks out the other side, the front chain ring sticks out.

- Brompton is useful partially-folded. With just the rear wheel tucked under it will stand up on its own. With just the seat or just the handlebars unfolded it can be wheeled around on the little roller wheels like a suitcase. It can be folded while leaving the front bag on without the bag going upside down, and with the bag accessible to wheel around using it like a shopping trolley.

- When folded, the top-tube of the bike is along the top of the fold, so is the seat, giving decent balanced places to lift and carry it like a suitcase.[4]

- One side has a folding pedal to tuck it away. The other side doesn't. I just think it's neat.

- Maybe goes without saying, but it can be folded without tools instead of being disassembled. Full size bikes can have joints in the frame so they come apart for packing for travel, but you just get a pile of separate pieces. Some medium size folding bikes need a wheel removed and only really fold for packing into a car, rather than something you'd do on the fly for a train trip. "Folding bikes" is not unique to Brompton, but in the market of "all bikes which can be made smaller", folding was a thing Brompton made mainstream, partly by inventing a fold that was so convenient.

[1] https://photo.velo101.com/wordpress/2022/09/DSC_6300-scaled....

[2] https://bikepacking.com/wp-content/uploads/2022/08/Bike-Frid...

[3] https://www.cyclox.org/wp-content/uploads/2022/10/Brompton-f...

[4] https://cdn.mos.cms.futurecdn.net/kA2bWNiWVEEKVTYBQgqbw9-102...