Just Google “R’lyehn alphabet” and the key will come up. There are multiple versions though. Here is one:
Usually such alphabets are created for role playing games, but also pop culture (Klingon), and novels (Tolkein’s Elvish). They can be used magically, to give a more arcane feel to petitions and such. They hold power because many people believe they do, and like other magical scripts, they can be fun to use.
Edit to add: It’s also possible that the script in the image was completely made up by the artist and is just meaningless gibberish. That image was created by an artist named Daniel Govar on DeviantArt.