The answer somewhat depends on which project template you select. (Empty, Internet Application, or Intranet Application)
If you select Empty, the checkbox adds the following two lines to the <head>
section in your _Layout.cshtml.
<meta charset="utf-8" />
<script src="@Url.Content("~/Scripts/modernizr-1.7.min.js")"
type="text/javascript"></script>
If you select Internet or Intranet Application, then in addition to the two lines above, you will see HTML5 semantic markup tags instead of divs in your _Layout.cshtml markup shown below:
HTML5 Box Checked vs. Not Checked
<header> <div id="header">
<nav> <div id="menucontainer">
<section id="main"> <div id="main">
<footer> <div id="footer">
I see no reason not to check it, but it does not really matter. As mentioned by Darin, the checkbox value is just for determining which markup is generated for you. The value is not stored in your project.
You can read more in Scott Gu's blog post:HTML5 Improvements with the ASP.NET MVC 3 Tools Update