What does it mean to lean on ouir own understanding?

First let us understand that our own understanding comes from a heart that is deceitful above all things, blind to its own faults, etc.

Jeremiah 17:9: "The heart is deceitful above all things, and desperately wicked: who can know it?"

Proverbs 14:12, Proverbs 16:25: "There is a way which seems right unto a man, but the end thereof are the ways of death".

As a result of being in the flesh, the natural man acts accordingly.

For a regenerate man the following it true:

Proverbs 16:9: "A man’s heart devises his way: but Yehovah directs his steps".

Job 32:8: "But there is a spirit in man: and the inspiration of the Almighty giveth them understanding".

We need to look outside of self to our God and Father Yehovah, and not lean on our own faulty understanding of things, for Yehovah knows the end of a matter from the beginning. 

Job 12:13: "With Him is wisdom and strength, He has counsel and understanding".

How do we begin to get right understanding?

Proverbs 9:10: "The fear of Yehovah is the beginning of wisdom: and the knowledge of the holy is understanding".

Psalm 111:10: "The fear [reverential awe and respect] of Yehovah is the beginning of wisdom: a good understanding have all they that do his commandments: his praise endures for ever".

Psalm 119:130: "The entrance of your words gives light; it gives understanding unto the simple".

Proverbs 2:6: "For Yehovah gives wisdom: out of His mouth comes knowledge and understanding".

Jesus didn't do anything without the guidance and direction of his God and his Father Yehovah whose Spirit was in him without measure.

John 5:19: "Then answered Jesus and said unto them, Verily, verily, I say unto you, The Son can do nothing of himself, but what he sees the Father do: for what things soever he does, these also does the Son likewise".

John 5:30: "I can of mine own self do nothing: as I hear, I judge: and my judgment is just; because I seek not mine own will, but the will of the Father which has sent me".

Jesus did nothing without being in subjection to his Father's will. He carried out to perfection the commission he had been given and when he had done all he cried out "It is finished". What an example for all of us who are in Him!

John 6:63: "It is the spirit that quickens; the flesh profits nothing: the words that I speak unto you, they are spirit, and they are life".

In the flesh and on our own we can not have the right understanding on how to proceed according to the will of our God and our Father Yehovah. Only as we maintain close communication with Him in prayer, seeking to have more of the direction of His holy spirit and submitting to the spirit guidance, can we achieve real and true understanding in order to  conduct our lives according to His will. May our God and our Father Yehovah give all of us more of His spirit to carry out all He has called us to do!