Tubular tires are no mystery. The tire casing encloses an inner tube (think donut shape), which is glued to the rim. A clincher tire is open (or U-shaped), the tire bead hooks onto the wall of the rim and secured with an inflated inner tube.
A tubular tire is completely round giving is a constant casing radius which gives a tubular tire advantages over a clincher tire.
1. Cornering is more predictable, there are no sudden transitions in traction.
2. The shock absorption is improved because road bumps are spread over the entire base on the rim.
3. Tubular tires can handle a much higher inflation pressure.
4. Tubular tires are more resistant to pinch flats. (watch this video of Paris Roubaix)
Cyclist and triathletes who ride tubular tires prefer them because tubulars feel better and ride faster. A clincher tire has the advantage of convenience, but a tubular tire delivers the best ride, lowest weight and remains the choice of top cyclist and triathletes.