An informal intensifier meaning 'extremely' or 'to death' used to exaggerate emotional or physical degree (can be used for both positive and negative feelings).
彼のことが死ぬほど好きだ。
I like him like crazy (I love him extremely).
この仕事は忙しくて、死ぬほど疲れた。
This job was so busy I was exhausted to death.
夏は死ぬほど暑くて、外に出たくない。
Summer is so hot I don't want to go outside.
あのケーキは死ぬほど美味しかった。
That cake was insanely delicious.