You can destroy Monster Nests just like in Witcher 2. Crafting or Buying Bombs and using them on the Nests.
In the Witcher 3 it works the same way you have to blow up the nests but with some new twists. Before you would go to the nest and press a button to drop the bomb.
Now in the Witcher 3 you can throw a bomb towards the nest or use a destructive sign at it to destroy it (You can try Aard or Igni (will try to confirm Igni on some nests later)).
"look around the chamber until you spot the two smoking mounds lying either side of the pit. As instructed, use either bombs or one of your destructive spells to obliterate them" - Quote from Guide
The specific bomb to destroy nests in the Witcher 2 was the Grapeshot Bomb.
EDIT:
Ghouls Nests and Nekker Nests can only be destroyed with bombs. Get a Samum Bomb or Grapeshot Bomb (Most Common) and go to the Nest and will ask you to press a button to drop de bomb just like in Witcher 2. Some nests can be destroyed by using the bomb and Igni and some only with Igni.
Endrega nests (Eggs) can be destroyed using Igni and so can rats nests.
If you need to replenish your bombs just meditate with Strong Alcohol like Alcohest and they will refill along with your potions.