What is the meaning of [Green-eyed monster]

Jealousy.
Green is a colour associated with sickness, possibly because people’s skin sometimes takes on a slightly yellow/green tinge when they are seriously ill. Green is also the colour of many unripe foods that cause stomach pains.

The green-eyed monsterThe phrase ‘green-eyed jealousy’ was used by, and possibly coined by, Shakespeare to denote jealousy, in The Merchant of Venice, 1596:

Portia:
How all the other passions fleet to air,
As doubtful thoughts, and rash-embraced despair,
And shuddering fear, and green-eyed jealousy! O love,
Be moderate; allay thy ecstasy,
In measure rein thy joy; scant this excess.
I feel too much thy blessing: make it less,
For fear I surfeit.