Your content is actually stored in the database. While you have the physical files that you need, the database on your local pc doesn't have any of the content (posts, pages, media links, etc...) in it that your live site does.
You'll need to download a backup copy of your live sites database. Once you have that, you can use a text editor to search and replace any references to your live site urls with your local site urls.
Example: search and replace all references to //www.yoursite.com with //localhost if that's your local install address. Then import the backup copy of the database into your local installation and things should probably be working on your local pc much like they do on the live site.