The code at first looks terrible. Let simplify it step by step.
//find 1st <button> element and assign on'click' handler to it
document.querySelector("button").addEventListener("click", function(){
  document.body.style.background = randColor();
  //background is the **result** of execution of randColor()
})
function randColor(){
  return '#' + (function co(lor){   return (lor +=
    [0,1,2,3,4,5,6,7,8,9,'a','b','c','d','e','f'][Math.floor(Math.random()*16)])
    && (lor.length == 6) ?  lor : co(lor); })('');
}
randColor() returns an expression which includes a function (in fact, IIFE).
Let put the result instead of function call. Meanwhile, parenthesis around the function can be omitted here because of + operator before.
document.querySelector("button").addEventListener("click", function(){
  document.body.style.background = '#' + function co(lor){
   return (lor +=
    [0,1,2,3,4,5,6,7,8,9,'a','b','c','d','e','f'][Math.floor(Math.random()*16)])
    && (lor.length == 6) ?  lor : co(lor); }(''/*send empty string to lor parameter*/);
})
Still not easy? Let's take next step.
document.querySelector("button").addEventListener("click", function(){
  document.body.style.background = '#' + co(''/*send empty string to lor parameter*/);
})
function co(lor){
   return (lor += /*assignment returns the new value. always truey in this case*/
    [0,1,2,3,4,5,6,7,8,9,'a','b','c','d','e','f'][Math.floor(Math.random()*16)/*magic 16 is the array length*/])
    && (lor.length == 6) ?  /*returns when we have 6 character string*/lor : /*call the function recursively*/co(lor); 
}
And final simplification. Use a loop instead of recursion.
function co(){
   var lor = '';
   var hexDigits = '0123456789abcdef'.split('');
   for(var i = 0; i < 6/*required length*/;i++){
     lor += hexDigits[Math.floor(Math.random() * 16)/*0 - 15*/];
   }
   return lor;
}
Leading # makes up correct HEX value for the color.