A distelfink is a goldfinch, literally a "thistle finch," and they most closely resemble a European variety (Image 2). There's a debate as to whether the drawn birds are just decorative (a passing down of imagery) or actually symbolic. The latter camps says they represent happiness and good fortune, and I'm inclined to stick with that. Distelfinks accompany hearts, angels, and tulips as decorative elements in Fraktur, a type of illuminated folk art that recorded major life events such births, baptisms, and weddings. Primarily Lutheran and Reformed church members created these manuscripts, which were usually family-focused and religious. Apparently, though, if you had an ambitious lover or were a good student, you might get one too.
Handwritten Fraktur, done in a "broken" style of calligraphy of the same name, was prevalent from about 1750 to 1850, and their decorative elements persist today in hexes. Hexes' purpose has changed over time between possible charm, cultural symbol, and tourist good. Hexe means "witch" in German, and in my reading I was really surprised to learn about spielwerk, essentially Pennsylvania Dutch magic. If you're curious, you can read more in Hex and Spellwork: The Magical Practices of the Pennsylvania Dutch. It's worth noting that the folk art scholar who says distelfinks, et cetera, are not symbolic also rejects the idea that hexes had magical significance.
Superstitions and charms aside, hexes' earlier popularity might have been due to efforts by Pennsylvania Germans to protect and promote their culture (the dialect, for example, has not been widely spoken outside Amish communities since the 1950s). Traditionally hexes have been painted onto the side of barns, but these days you'll also find distelfinks on plaques that can be attached wherever you see fit.
While such hexes are readily available for purchase in Lancaster County, it bears pointing out that neither the Amish nor Mennonites use them (although both did make Fraktur). Those groups are referred to as "Plain Dutch," as manifested by their clothes, while the makers of hexes have different religious beliefs, have become more integrated, and are called "Fancy Dutch." (I'm German by ancestry, but we don't fall into either category. Also, the "Dutch," is really "Deutsch" or "Dietsch.")
Finally, while the look of Fraktur isn't for everyone, know that a "masterpiece" handwritten manuscript can fetch hundreds of thousands of dollars. Also, you can find updated takes on traditional Pennsylvania German designs and crafts by artists such as the ones who make up Z-Town Made Craft Collective (Images 7-10) from Kutztown, PA.