Robert Frost's poem "Out, Out-" alludes to Macbeth's soliloquy in Act Five, Scene 5 of the play Macbeth. In Macbeth's soliloquy, he comments on the death of his wife and analyzes how insignificant our lives are in the grand scheme of the mysterious universe. Macbeth says,

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, Signifying nothing. (Shakespeare, 5.5.23-28)

Macbeth mentions that his wife was bound to die someday and compares one's existence to a "poor player," who struts around on stage for an hour before he is heard from no more. Macbeth goes on to say that life is void of meaning and compares it to a "tale told by an idiot." Macbeth's nihilist, absurd view of life is a result of his hopeless perspective of his future.

Robert Frost's poem is about a young man, who gets distracted by his sister's call for supper and accidentally cuts his hand with a saw. After begging his sister to tell the doctor not to amputate his hand, the boy dies from blood loss while under anesthesia, and everyone goes back to work. Similar to Macbeth's soliloquy in Act Five, Scene 5, Frost's poem portrays life as relatively meaningless, which is represented by the random, arbitrary way the innocent boy dies and the reaction of the other workers, who immediately resume what they were doing before the boy's accident. The nihilist nature of the poem and Macbeth's soliloquy correspond and depict life as trivial, insignificant, and absurd.

The allusion to Macbeth refers to obsession with blood and guilt.

An allusion is a reference to history or another literary work.  Allusions to Shakespeare are common, as

Shakespeare had a great influence on future writers.

The speech being referred to is the famous sleepwalking soliloquy scene from Act 5, where Lady Macbeth succumbs to guilt over causing the king’s death and creating the monster her husband has come.  Lady Macbeth sees the blood on her hands, metaphorically, and she cannot clean it off.

Out, damned spot! Out, I say! One–two—

why then ’tis time to do't. Hell is murky. (Macbeth, Act 5, Scene 1)

Despite the fact that this allusion is most easily recognizable as traced to Lady Macbeth, the soliloquy where Macbeth echoes her words also could be the reference in the poem.

Out, out, brief candle!(25)

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,

Signifying nothing.(30) (Macbeth, Act 5, Scene 5)

There is less of guilt than recognition in the poem, when blood is described.  It is an acknowledgement that life is pointless, and there is nothing that can be done.

No one believed. They listened to his heart.

Little—less—nothing!—and that ended it.

No more to build on there. And they, since they

Were not the one dead, turned to their affairs. ("Out, Out-")

A boy is dead, and everyone goes about their business?  It seems like Macbeth was right.  There is nothing to life but a “walking shadow” that means nothing.