It means that those who are not without mistakes themselves, should not judge others. For example, a mother who didn't raise her kids well should not judge other mothers who failed to properly raise their kids. Or: A corrupt politician should not judge other people for being corrupt. You can apply this to about everything. The next time you criticize something just think to yourself if you're without fault. A single word you can connect to this idiom is "hypocrisy". Hope this helps. :)

It means do not criticize another person before you look to your own beam in your eye. In other words don't criticize other people.

I would add to what already stated that the lesson of this sentence is: For human being it's easier to see the other's faults and defects than the ones of his own

The pot calling the kettle black.