You can make it visible by adding new web part on the page which contains simple javascript code that will show your description.
First, I will create new site with some description:
Now, open your site on which you need to add description and click on Settings --> Edit Page:
In SP Ribbon click on tab "Insert" and then click on button "Web Part". Add new web part called "Script Editor" from "Media and Content" category:
Edit that Web Part and copy following script in it:
<script>
_spBodyOnLoadFunctionNames.push("GetSiteInfo");
var site;
function GetSiteInfo()
{
var ctx = new SP.ClientContext.get_current();
site = ctx.get_web();
ctx.load(site);
ctx.executeQueryAsync(onQuerySucceeded, onQueryFailed);
}
function onQueryFailed(sender, args) {
alert('request failed ' + args.get_message() + '\n' + args.get_stackTrace());
}
function onQuerySucceeded(sender, args) {
var desc = document.getElementById('divSiteDescription')
desc.innerHTML = site.get_description();
}
</script>
<div id='divSiteDescription'></div>
Save Web Part changes and save changes made on the page by clicking button "Save" in SP Ribbon.
Now, you can see the description of your site on the page: