There are two famous passages in Macbeth that possess universal significance. One of them is to be found in Act 2, Scene 2. Macbeth has just murdered Duncan and is talking to his wife.
Methought I heard a voice cry 'Sleep no more!
Macbeth does murder sleep', the innocent sleep,
Sleep that knits up the ravell'd sleeve of care,
The death of each day's life, sore labour's bath,
Balm of hurt minds, great nature's second course,
Chief nourisher in life's feast,--
We can all relate to the metaphor describing sleep, especially "the death of each day's life." Going to sleep is very much like dying. Hamlet says in Act 3, Scene 1 of that play:
To die: to sleep;
No more; and by a sleep to say we end
The heart-ache and the thousand natural shocks
That flesh is heir to, 'tis a consummation
Devoutly to be wish'd.
Shakespeare apparently loved sleep. He wrote about the pleasure of sleep in Henry V and in some of his sonnets.
Macbeth is horrified by the thought that he might never be able to sleep again because of the crime he has committed. We can all imagine how terrible that would be, because we all have bad nights when we would love to be able to fall asleep and forget our problems for a whole blissful night. Waking up in the morning is like being reborn, so each day is like a lifetime in miniature: being born in the morning, going out into the world with all its troubles and conflicts, coming home in the evening, which is like going into retirement, then falling asleep, which is like dying and forgetting everything.
Another passage with universal significance occurs near the very end of Macbeth, in Act 5, Scene 5, when Macbeth has been informed that his wife is dead. He is already feeling so utterly depressed that more bad news could hardly make him feel any worse. He is all alone and facing certain defeat by the invading English army.
To-morrow, and to-morrow, and to-morrow,
Creeps in this petty pace from day to day
To the last syllable of recorded time,
And all our yesterdays have lighted fools
The way to dusty death. Out, out, brief candle!
Life's but a walking shadow, a poor player
That struts and frets his hour upon the stage
And then is heard no more: it is a tale
Told by an idiot, full of sound and fury,
William Faulkner, the great American novelist, borrowed the phrase "sound and fury" for the title of one of his earlier novels, The Sound and the Fury. Faulkner must have agreed with Shakespeare that life is meaningless, that people go through all sorts of quarrels and enterprises inspired by greed and vanity and end up with nothing because they all have to die sooner or later. "Man born of a woman hath but a short time to live, and his days are filled with misery," as the Bible says. And elsewhere the Bible says: "Vanity of vanities, all is vanity."
The metaphor beginning with "Out, out, brief candle!" is more complex than at first meets the eye. Macbeth is wishing that the candle would go out because it is the candle that is creating the shadow. "Life is but a walking shadow" because something else is creating the light that casts the shadow. Plato says something very much like this is his famous allegory about the people in the cave in The Republic.
These are the two best quotes from Macbeth in answer to your question about universality. Not everybody would agree with the one about life being meaningless, but everybody will agree that sleep is a blessing, that it is "innocent" and the "chief nourisher in life's feast."