If you had used blank site
as template in your SharePoint 2010 than that will not be available.
If you had used Team site
as template in your SharePoint 2010 than you will get Edit Links
option in both menus.
Please check below reference link.
Migrating SharePoint 2010 to SharePoint 2013 navigation Edit links option not available / missing
UPDATED
The old “Navigation” option in Site Settings still exists for editing Quick Launch and Global Navigation.
IF you want to change the navigation only than you can do it from Site Settings > Look and Feel > Navigation.
The Feature is available Only for sites with Publishing feature turned on.
Hide all site content from quick launch SharePoint 2013 with CSS
Edit your SharePoint page, Insert a "Script Editor" web part and add the below code in it (For Specific Page).
<style>
#sideNavBox a[href$="/_layouts/15/viewlsts.aspx"]
{
display: none;
}
</style>
To remove site content from quick launch of SharePoint 2013 sites, Add this CSS to master page, Or you can have it in Alternate CSS sheet.
if & only you change the site template.
....i thought about it, but no idea how to do it.