What is the purpose of template literals (backticks) following a function in ES6?

These are tagged template literals. The part before the backpacks is a reference to a function that will be called to process the string.

The function is passed the variables (the ${} parts) as arguments as well as the pieces of the string that surround the variables broken into an array. The return value of the function becomes the value of the template. Because of this very generalized format, you can do almost anything with the function. Here's a quick and dirty example that takes the variables (gathered into an array for convenience), makes them uppercase, and puts them back in the string:

function upperV(strings, ...vars) {
  /* make vars uppercase */
  console.log("vars: ", vars)       // an array of the passed in variables
  console.log("strings:", strings)  // the string parts

  // put them together
  return vars.reduce((str, v, i) => str + v.toUpperCase() + strings[i+1], strings[0]);
}

let adverb = "boldly"
let output = upperV`to ${adverb} split infinitives that no ${'man'} had split before...`;
console.log(output)

Template literals have an additional feature called tagged templates. That's what the prefix before the opening backtick is. The prefix is actually the name of a function - the function is passed the constant parts of the template strings and the interpolated values (stuff in the ${} sections) and can process the resulting string into whatever it wants (although generally another string, doesn't have to be).

See this page on MDN for more details on how tagged templates work.