The Seiko Museum Ginza: "The balance wheel is a mechanism that, while possessing the same isochronous quality as the pendulum, is not so susceptible to vibrations and is therefore portable." That portability is why wristwatches exist.
Its construction, per the same source: "a fine 'hairspring' fitted into a metal wheel, with one end of the spring fixed to the wheel and the other fixed to the body of the timepiece."
Isochronism is the property that makes it work: "The hairspring is isochronous, so the cycle remains unchanged even when the oscillation angle shifts." The swing can vary in size without the period changing much, which is what lets a watch keep time as its mainspring runs down.
Grand Seiko on the balance's place in the system: "This regular oscillation is transferred to the pallet fork, which controls the rotation of the escape wheel at a constant rate… The hairspring is the critical component at the heart of a mechanical watch as it governs its precision."