Typically, to sink your teeth into something is to really muster your powers and/or energy either to understand something or to get a good grip mentally, emotionally, and perhaps even physically of something. Similar idioms include digging deep as in digging deep for the solution.
i.e. She finally sank her teeth into the crux of the problem and was able to find a resolution that satisfied both parties.
On the other hand, to sink your teeth into something may also imply having a rather voracious appetite, and consequently the quick and plunging sinking of your teeth into whatever food hits the spot.
i.e. My sister sank her teeth into the brussel sprouts (weird), while my brother sank his teeth into durian fruit (weirder).
Durians. Spiky, eh?
Hedgehogs. Cute, right?
Dur-hog or Hedge-ian, otherwise known as a Durian-Hedgehog hybrid. (weirdest)
Eric
