Explain with reference to context the following lines from Hamlet.
'Tis now the very witching time of night, When churchyards yawn and hell itself breathes out Contagion to this world. Now could I drink hot blood And do such bitter business as the bitter day Would quake to look on.
In Shakespeare's Hamlet, the lines you quote are from Act 3.2.356-360.
Before Hamlet speaks these lines, he gets the proof he's been waiting for that the Ghost is telling him the truth and that Claudius is definitely guilty of assassinating King Hamlet.
In these lines Hamlet emphatically claims that he is now ready for action. He's ready to get revenge and kill Claudius.
Specifically, Hamlet says that it is the witching hour, the dead of night, the time of night when graves and graveyards open and hell breathes stench upon the world. Now could he drink hot blood and do things (like kill Claudius) that the day would be afraid to look at.
Of course, Hamlet doesn't immediately act and get his revenge. He has an opportunity when Claudius is alone and praying, but Hamlet does not want to send Claudius to heaven by killing him just after he's confessed his sins. By failing at this point, Hamlet brings about the catastrophe at the conclusion of the play, resulting in many more deaths than necessary.
These lines are spoken by Hamlet in Act III, Scene 2 of the play. Here is what he means, more or less.
This is the time of night when the witches come out.
It is the time of night when graves open up and you can even smell the stink of hell breathing disease into the world.
Because it is night, I could do terrible things. I could drink hot blood (meaning from things that aren't dead) and do other stuff that even the daylight would be horrified by.
But instead of actually doing stuff like that, he's going to go see his mother. He says he won't actually do anything horrible to her -- just use harsh words.
These lines occur in Hamlet's soliloquy in Act III Sc.2. During the performance of the play King Claudius' conscience is pricked and he exposes himself by getting up half way through the play and going away. Hamlet is now convinced that what the ghost had told him is true and that Claudius has murdered his father:
Hamlet is excited and decides to kill Claudius. At the end of the scene when he is all alone he utters these lines:
Tis now the very witching time of night,
When churchyards yawn and hell itself breathes out
Contagion to this world: now could I drink hot blood,
And do such bitter business as the day
Would quake to look on.
These lines express Hamlet's passionate desire for revenge; he means to say that he is bloodthirsty and that he is ready to kill Claudius and drink his blood and that he is now prepared to do the most horrific things ever.
Shakespeare's plays were mostly performed in the afternoons on stages which were open to the sky. The stage props were very rudimentary. This was compensated for by the purple poetry of Shakespeare which created the necessary drama and atmosphere. Hence the verbal bombast and the highly ornate description of the night to remind the contemporary audience - who will be watching the play in the afternoon - that this scene is taking place in the night.