the equations for phase-change phenomena generally assume that nuclei are present. this works in theory but in practice the absence of nuclei will seriously skew the real-world results, throwing experiment and theory apart. this is true for liquid-vapor, vapor-liquid, and liquid-solid phase changes.
Here is why nucleation sites work:
in each case, the nucleation site, for a variety of (physical chemistry) reasons, presents itself to the nonequilibrium bulk phase as a pre-existing example of the impending phase change, and thereby "seeds" the phase change by furnishing a site that "looks" like the outcome.
for example, an air bubble in a crevice in the bottom of a boiling vessel resembles a vapor bubble, and its presence in the (superheated) liquid gives an excuse to the liquid molecules in its immediate vicinity to join in the action and vaporize into the bubble.
similarly: in the case of supersaturated water vapor condensation onto a solid surface, the condensation will preferentially occur at locations that are contaminated with tiny dust particles- because those particles have adsorbed water vapor from the air in advance and with their free surfaces densely populated with water molecules, they look like water droplets themselves.
in the case of exsolvation of CO2 bubbles from a supersaturated water solution in a container, the bubbling process will occur preferentially at pits, scratches and microcracks in the container walls because those sites contain tiny amounts of air that look like pre-existing CO2 bubbles. The people who set up photo shoots for beer commercials know this: If you pour beer into a brand new pilsner glass, you'll get almost no bubble streams rising up through the beer for the camera- you must first introduce microscratches into the glass walls by shaking the empty glass with a fistful of ball bearings in it first.