You can get rid of /_layouts/15/start.aspx in the URL by going to Site Actions -> Site Settings -> Manager Site Features -> Deactivate Minimal Download Strategy feature

However this is a new framework in SharePoint 2013, which increases performance of SharePoint site..

More reading here:

What is /_layouts/15/start.aspx

Why does /_layouts/15/start.aspx appear as part of SharePoint 2013 URL