Exactly what is sounds like - a torch made of cardboard.
This is not extremely dangerous, but there is a good chance you will get a few very minor burns if you aren't careful. The biggest concern is accidentally starting a fire because burning chunks of cardboard often come loose.
These torches are difficult to extinguish and easy to keep lit. They last 3-10 minutes. If it is smoking, it has a STRONG possibility of self-ignition. To kill it, unravel it or dip it in water.
This will make you smell terrible and put off a lot of smoke.

Step 1: Materials

Corrugated cardboard (any broken-down box will work)
tape/glue (any tape will work, but masking tape is best for a natural burn in this situation)
lighter and candle

I recommend a wide open environment and a bucket of water.

Step 2: Roll the Cardboard

Roll the cardboard so that the corrugation is parallel to the direction of the roll. (this will augment air flow)
Leave slightly less than one inch of space in the center, and roll tightly around that. For best results, there should be about 5-7 layers of wrapped cardboard.

Step 3: Secure the Roll

Tape the bottom, middle, and near top to keep the cardboard rolled.
Alternatively, leave a strip of glue in the penultimate wrap and rubber band it until it is dry.

Step 4: Ignite!

This is surprisingly the hardest part.
The rolled cardboard is difficult to light for the same reason it is difficult to put out.
Here's my method:
Use a wax candle to burn a hole in the top of the inside.
Turn it over and drip melted wax onto the same spot.
Ignite the waxed spot and let it burn the rest of the inside as you slowly turn it, burning the entire interior.
Wait a while until it becomes a sustainable flame and then swing it around to augment air flow.

Alternatively, dip the tip into a liquid accelerant and ignite.

Step 5: Burn!

Give yourself plenty of space.
- Swing it around to fuel the inferno.
- Hit something to throw sparks.
- Swing it more to relight it.
- Blow through it to create a flamethrower.
- Slow it down by dipping the tip in water
- Douse it by submersing in water for several seconds.
Don not leave unattended - they will self-ignite.
Please be relatively safe.

Step 6: Keep in Mind Some Dangers:

Wind will probably blow the ashes toward no matter which way you face since your figure blocks the wind creating an low-pressure vacuum.
Realize that with a spear- thrust motion, it is entirely possible for the flames to come out of the wrong side. (don't put your hand there)
People die from smoke inhalation more often than from fires - this is not a large cigarette.
As it gets short, it is possible for a larger chunk of burning cardboard to fly off as the remainder of a whole layer is burned off.

Step 7: For Optimization...

Obviously, the torches are not reusable, but for next time:
If the center burned down too quickly, make the center smaller next time.
If it took to much swinging around to get a good flame, make the center larger.
If it came apart early, move each piece of tape closer to your hand.