How to change background color by click with javascript?

The way you were setting the onClick handler was wrong.

document.getElementById("trying").onclick = function(){
    var someText = document.getElementById("textArea").value;
    document.getElementById("randomText").innerHTML = someText;
}

function getRandomColor() {                
    var letters = '0123456789ABCDEF'.split('');
    var color = '#';
    
    for (var i = 0; i < 6; i++ ) {    
        color += letters[Math.floor(Math.random() * 16)];
    }
    
    return color;
}

document.getElementById("mainBox").onclick = function() {
  document.getElementById("mainBox").style.backgroundColor = getRandomColor();
}

.mainBox {
				width: 400px;
				height:350px;
				background-color:pink;
				margin-right:auto;
				margin-left:auto;
			}
			#textArea {
				margin-left:100px;
			}

<div id="mainBox" class="mainBox">
				<p id="randomText" align="center">U know who you are?</p>
					<input type="text" id="textArea">
					<button id="trying">Try it!</button>
				</div>

I notice you have all your code in one place separate it. If you don't adhere to encapsulation you can get into a lot of trouble. Separate your code and things will be much easier for you. You were just missing a bracket, also try to form your answers a little bit clearer to avoid getting down voted ;). Also, we you have to fix your code so that the words don't disappear, i'll let you figure that out on your own.

Simple way to understand Encapsulation and Abstraction

http://codepen.io/psikosen/pen/RGPkAv

html
<div id="mainBox" class="mainBox">
                <p id="randomText" align="center">U know who you are?</p>
                    <input type="text" id="textArea">
                    <button id="trying">Try it!</button>
                </div>
css
 .mainBox {
                width: 400px;
                height:350px;
                background-color:pink;
                margin-right:auto;
                margin-left:auto;
            }
            #textArea {
                margin-left:100px;
            }


Js
document.getElementById("trying").onclick = function(){
    var someText = document.getElementById("textArea").value;
    document.getElementById("randomText").innerHTML = someText;
}
document.getElementById("mainBox").onclick = function() {
  document.getElementById("mainBox").style.backgroundColor = getRandomColor();

function getRandomColor(){

    var letters = '0123456789ABCDEF'.split('');

                var color = '#';

                for (var i = 0; i < 6; i++ ) {

                    color += letters[Math.floor(Math.random() * 16)];

                }

                return color;
}

}