So, is Nidhug trying to destroy Yggdrasil?
The story of Yggdrasil is long and complicated. It's the tree of life and all other things exists around Yggdrasil. Including the 9 realms and earth is one of those realms. The tree binds it all together in a way. The dragon Nidhug is in a realm called Niflheim, it means World Of Mist. The dragon is a vicious beast and it is trapped there, Yggdrasils roots is blocking the way, keeping him down there. So that's why he is gnawing at the roots.
The name Nidhug means Malice Striker and that dragon is associated with villains and loss of honour. Hel is also underneath that tree, in Hel there is a place called Nástrǫnd (Corpse Shore), that's Nidhugs home and a part of Nidhugs job is to chew on the corpses of murderers, adulterers and oath breakers.
There is also a squirrel involved in all this, on top of that tree sits an eagle. And a squirrel called Ratatosk (Bore-Tooth) runs up and down the tree, delivering gossip and messages from the eagle to Nidhug.
That's the short version, a lot going on there, it's a very big tree.
