Rooted in the 18th century royal courts of Italy and France, ballet is a dance form that historically valued a light, airy feel. For that reason, it's often considered an effeminate pursuit. Although strength and athleticism are increasingly important in ballet, there remains a demand that dancers, particularly female, exhibit an almost other-worldly grace.
The intricate courtly footwork of early ballet evolved into dancers stretching and arching their feet into impossibly extended forms, creating the illusion of legs that went forever. Those pointed feet later inspired ballerinas like Marie Taglioni to dance on the very tips of their toes. Taglioni's dancing, executed without the benefit of modern pointe shoes, is quite impressive, as it was astonishingly light and would have been very painful.
Today, both male and female dancers usually begin class with 30-60 minutes of "flat work" or "technique" to warm up their feet before the women trade their soft ballet slippers (canvas or leather, like those you see on small children) for their sculpted, satin pointe shoes. The pointe shoe is designed to provide a hard, square box, which ballerinas stuff with lamb's wool and other cushioning materials, and on which the ballerina can more easily stand and balance. The shank along the sole of the shoe provides support for the ballerina's arch, helping her to spring up and down on her toes.
Despite the significant advances in pointe shoe design in the last hundred years or so, the shoes don't protect ballerinas from chafing and blistering, digging and bleeding, and squeezing and malformation. The feet, ankles, calves, knees, hips and abdominals must be very strong before a dancer is ready for pointe work. And then she can expect a lifetime of cramping arches, swollen toes, scraped heels and misshapen bones in her feet.
The miracle of pointe work is the blood and sweat that goes into making it so incredibly lovely to see.