Albert Barnes on Matthew 7:3

And why beholdest thou the mote, etc. A mote signifies any light substance, as dry chaff, or fine spires of grass or grain. It probably most usually signified the small spiculae or beard on a head of barley or wheat. It is thus placed in opposition to the word beam.

Beam. This word here signifies a large piece of squared timber. The one is an exceedingly small object, the other a large one. The meaning is, that we are much more quick and acute to judge of small offences in others, than of much larger offences in ourselves. Even a very small object that should hinder the vision of another, we should discern much more quickly than a much larger one in our own sight. This was also a proverb in frequent use among the Jews, and the same sentiment was common among the Greeks, and deserves to be expressed in every language.