The first thing you have to understand is that when you type www.website.com into your browser you don't just immediately go to that website. Instead, your traffic passes through numerous routers, owned by different entities, before it finally gets to website.com, and then it has to come all the way back.

When your traffic passes through each router, it tells that router "I want to go to website.com and I come from TheJovSka's dorm room." Each router then does its best to send your traffic on so that it gets to where you want it to be.

It sounds like you're on your university's network, so they are going to own the first few routers before you actually reach the internet. So, for example, its likely that your traffic passes through a router in your building, which then sends it on to central router for the entire campus, which then sends it on to a router in "the internet."

Your university has set it up so that when its routers see traffic heading towards website.com they will ignore it, effectively preventing you from accessing website.com because all of your traffic has to pass through a university owned router.

Opera Turbo alters all of your traffic. Instead of sending your traffic to website.com, Opera Turbo sends the traffic to a website owned by Opera Software, and embedded in that traffic is an encrypted request to actually go to website.com. Because the request in encrypted, only you and Opera Software can read it and to your university all of your traffic looks like its headed to Opera Software (which they haven't blocked).

Once Opera Software receives your traffic, it forwards it on to website.com, but makes it looks as though the traffic is coming from Opera Software. Website.com then sends the traffic back to Opera Software, who then send the traffic back to you. Again, this makes it appear as though all of the return traffic to you is coming from Opera Software, rather than website.com.

And although this isn't necessarily part of your question, it does raise the issue of "who pays for this" - because it costs Opera Software a non-trivial amount of money to run this operation. The answer to that is Opera Software also runs two very large ad serving networks. They record all of your traffic, and then use that information to target ads to you over those networks.