What does the www8 or www6 in a URL mean?

The www part of a url is just a subdomain of the domain name. www is common but there's nothing special about it other than everyone knows about it. The people who run example.com could just have easily used wwwsix or wwweight or secure.example.com or mail.example.com or app.example.com, etc. They could use different sub-domains for different countries, like us.example.com, or fr.example.com.

"www" is just the name of the host or server for the website. You can have any name you like for your webserver, such as "mywebhost.example.com" but "www" is now such a well-known and understood convention for a publicly available worldwide web site that it would be very unusual to do so other than for very well known sites or internal-use hosts (such as an Outlook Web Access site - you might choose to use owa.example.com for your users to visit, separate from your company website).

So, since this is just a host name essentially it can be anything. Sites with multiple front end servers would usually hide these behind a single round-robin name such as www, but it is possible that you will be redirected to a specific host for things like downloads or media streaming. In this case www6 or www8 are probably just two servers in a large farm of hosts providing material to users on the worldwide web.