Tasks are little things your dragon can do to help around the clan. Maybe they clean the cookpot or help hunt. Whatever it is, your Ath will reward you for it.
Cleaning Up
Doing the Dishes
Straightening Up
Making Dinner
Finding Food
A Short Hunt
Calming the Hatchlings
Bedtime Story
Babysitting Duty
Helping Out the Elders
Keeping Watch
Tracking Down Lost Things
Holding Things
Helping Move Furniture
Replacing Damaged Furniture
Cleaning Up, Doing the Dishes and Straightening Up will all earn you 15 Triangle Tokens each. If you complete all three, you will also be awarded a trophy, "Neat Freak", and a silver ribbon.
Making Dinner, Finding Food, and A Short Hunt will all earn you, randomly rolled, a small bone, a bird skull, or a scrap of fur. If you complete all three, you will also be awarded a trophy, "Bottomless Stomach", and a warm pelt.
Calming the Hatchlings, Bedtime Story, and Babysitting Duty will all earn you scrap of fabric, yarn, or thread. These items will be randomly rolled unless you specify which you want. In addition, Babysitting Duty will earn you 15 Triangle Tokens. If you complete all of them, you'll also be awarded a trophy, "Not So Scary Now", and a soft plushie.
Helping Out the Elders, Keeping Watch, and Tracking Down Lost Things will all earn you, randomly rolled, a colorful flower, a tattered ribbon, or 5 Triangle Tokens. If you complete all of them, you'll be awarded a trophy, "Are You Sure This Is Your Problem?", and a battery-powered radio receiver that is missing its battery.
Holding Things, Helping Move Furniture, and Replacing Damaged Furniture will all earn you 10 Triangle Tokens and your choice of a damaged screwdriver, damaged hammer, or damaged gloves. If you complete all of them, you'll receive a trophy, "Not IKEA", and a partially-disassembled toolkit.
If you complete every prompt on the list, you'll be awarded a trophy, "Cooperative Clanmate", a rechargeable battery, and 250 Triangle Tokens.
If your character is already an Ath of a clan, you are unfortunately not allowed to participate in Tasks.
Your dragon is not allowed to intentionally mess up or cause mischief during the Tasks in order to qualify for their reward. Assume that you are being given these by members of your clan that you have helped. If you ran around kicking old ladies for the "Helping Out the Elders" prompt, you will unfortunately fail that prompt and not be given the reward. You will be awarded points for the work, however.