If you picture medieval England, Smith is the easiest surname to decode: it named the person who worked metal. In most villages that meant the blacksmith—the one who shoed horses, mended tools, and kept hinges from falling off doors. Because every settlement needed that skill, the label sprang up independently in place after place, which is why Smith became so common rather than pointing to one famous ancestor.
The English word sits in a big European family of metalworker names (think German Schmidt or French Lefèvre), but American Smiths mostly inherit the English occupational surname—or later adopted it. Spellings like Smyth and Smythe are the same name in fancier clothes. The meaning itself is not mysterious: before factories, the smith was infrastructure.