Well, I only copied it myself, but it's not that complicated. From the API docs we learn that we need our search terms both in verbatim and base64 encoded. The first $@ is the verbatim part, and the second one is the one involved in the base64 part.

$(<command>) gets replaced by the output of <command>, in our case that means the output of the openssl base64 call, which takes stdin, applies the base64 encoding and prints it out on stdout. echo -n $@ just serves to translate our parameters into something the openssl base64 call can work with (-n means it won't introduce a superfluous newline). I'm not sure why the script uses openssl base64 instead of just base64 (a GNU coreutils utility).

I agree with the sibling that the API requirement to include both verbatim and base64-encoded search terms are fairly bizarre.