Why does dissolved solute raise the boiling point?
Solute lowers the solvent's vapour pressure, and a liquid boils when its vapour pressure matches the air pressure - so it must be heated hotter to boil. The boiling point rises with the number of dissolved particles.
Does salt really make pasta water boil hotter?
Yes, but only by a fraction of a degree at cooking amounts (water's K_b is just 0.52). It does not noticeably speed cooking - salt is added for taste. The effect is real but small.
What is the boiling constant K_b?
A property of the solvent - degrees the boiling point rises per unit molality. For water it is 0.52, the boiling-point twin of the freezing constant K_f.
Where does this matter industrially?
Anywhere solutions are concentrated by boiling - sugar refining, condensed milk, salt production - because the boiling point keeps rising as the solution thickens. Engine coolant also uses it to resist boiling on hot climbs.
How does the example give about 0.52°C?
With K_b = 0.52 and m = 1, the rise is 0.52 × 1 = 0.52°C, so the solution boils near 100.52°C. For salts that split into ions you multiply by the van 't Hoff factor.