There are two ways to remove the Quick Launch in SharePoint 2013. The first is to open the site in Share Designer, and uncheck the option to "Display Quick Launch". While this works, it doesn't move the content to the left. You're left with an empty space that doesn't look great.
The second option is to alter the CSS using a Script Editor web part. Place a Script Editor webpart anywhere on the page, and add the following code. The first line removes the Quick Launch. The second line moves the code all the way to the left.
<style>.ms-core-navigation { DISPLAY: none }#contentBox { margin-left: 0px }</style>
The code presented above removes the Quick Launch but also removes the Global Navigation links from the top of the screen. If you just want to remove the Quick Launch the following code should do the trick.
Replace .ms-core-navigation with #sideNavBox