Special VFR can be used a few different ways.

If ATC allows, you can get a special VFR to depart an airport when the weather is less than VFR. Why would you want to do this? Suppose there is a solid wall of fog right at the airport and you just happen to be on the wrong side but just a few miles past the airport it goes to extreme clear (I've seen it and it's not TOO uncommon). You can special VFR it out of the airport to get to class G airspace where you are then legally allowed in lower airspace until you get to the clear air.

The other option was I used to fly out of a field with no instrument approaches but there was a class D just 7 miles away and I flew that route between the two constantly so I was very aware of the route. I even had a radial to follow. I knew the landmarks very well. So many times when coming home, I would file to the class D, shoot the approach, cancel IFR, then proceed visually to the destination airport. A few times I would have to request a special VFR to get out of the airspace and get to my destination.

However, since you are a student pilot I would be failing as a CFI if I didn't offer some warning. Special VFR means you will be flying when visibility is less than 3 miles. At 120 kts, that gives you a minute and a half to see and avoid obstacles at MOST. 2 miles you have less than a minute! First of all, as a student, I thought I was in IFR the first time I saw visibility less than 10 miles. As a student, you should see what lower visibilities look like and you realize how little there is at 3 miles.

But most important, I personally would never fly SVFR in an area I have not extensively flown VFR in (like my training airport). It's just too low and close to the ground for my liking.

Clear as mud?