“Do not judge, or you too will be judged.2 For in the same way you judge others, you will be judged, and with the measure you use, it will be measured to you. 3 “Why do you look at the speck of sawdust in your brother’s eye and pay no attention to the plank in your own eye?4 How can you say to your brother, ‘Let me take the speck out of your eye,’ when all the time there is a plank in your own eye?5 You hypocrite, first take the plank out of your own eye, and then you will see clearly to remove the speck from your brother’s eye."
We've all heard the phrase "it's not my place to judge." And while it's often true, it's not always true. Jesus' didn't leave the phrase "do not judge" by itself...he made a condition of it: if you do choose to judge someone, be prepared to be judged yourself.
Jesus is not suggesting that there is never a time or a place or a situation to make moral judgments about someone, he's suggesting care about doing so and an awareness first of our own sin. If we aren't willing to be aware of our own sin and allow God to help us deal with it, then we have no place to use our critical faculties towards someone else. However, there is a time and place for us to "take the speck" out of someone else's eye...but only after we have taken the "plank" out of our own eye.
At the same time, it is definitely a warning not to be harsh towards people...especially people who have not given us permission to hold them accountable.
We all need someone (or several "someones") that will challenge us when we are living in a way that is harmful to ourselves or to someone else. When we hold someone accountable it can look a lot like judgment, but if they have given us permission to call them out then we need to do just that. It's the people who haven't given us that permission that we have no place to judge...especially if we haven't taken the time and effort to name and deal with our own sin.
I also believe Jesus is using humor here to make his point. A plank in someone's eye is a pretty funny image if you think about it:
Jesus' point is be careful about judging other people...because you have some things you need to deal with yourself.