This is a quotation of Jesus from Luke 6:41 in the Bible. Verse 42 goes on: "How can you say to your brother, 'Brother, let me take the speck out of your eye', when you yourself fail to see the plank in your own eye? You hypocrite, first take the plank out of your eye, and then you will see clearly to remove the speck from your brother's eye." A similar passage appears in Matthew 7:3-5.
Jesus was using hyperbole (an exaggerated example) to show how hypocritical it is for us to criticize someone for a minor fault (represented by the speck of sawdust in your brother's eye) while remaining blind to our own considerable faults (a whole plank of wood in your own eye).
The NIV Study Bible.