Integrity is one of those character traits that is often both lauded and mourned. People praise it when it's seen (sometimes, depending on how it's shown or what it's shown over, however, it's maligned) and many (usually older generations and some fundamentalists) mourn its apparent demise.
But, what is it?
People often describe integrity as "being the same person that you are in public when no-one's around." It's a good working definition, but it's lacking some soundness. Being the same person publicly and privately is merely an aftereffect of integrity.
Buildings are said to have integrity or to have their integrity compromised. What do people mean when they say this?
Well, structural integrity is built off of two key factors: the quality of the foundation and the quality of materials.
A foundation lacking integrity lacks stability. It shifts and warps with the seasons, weather conditions, and age. Any homeowner dreads to hear that their foundation has shifted as the stability of the house is compromised. Cracks creep up walls; leaks develop; or floors could cave in. It doesn't matter what the house is built from, if the foundation isn't secure, if it doesn't have integrity, the house is doomed from the start.
Integrity-less building materials lack strength. They can be soft, porous, untreated, etc. As time and wear buffet a structure made of weak materials, breakage and rot sets in. Soft bricks erode and crack from the weather and strain; untreated and unprotected wood warps and rots; and porous or hollow materials begin to harbor pests or fungi. The house can no longer protect its inhabitants. It becomes a danger to its owners. It breaks down regardless of how well set its foundation is.
The same goes with personal integrity. Personal integrity stems from a firm foundation and material strength (aka strength of character).
Each of us needs to firmly establish our foundation, our worldview, such that we won't find ourselves shifting and our entire character/definition falling apart. Church, one of the reasons many individuals of my generation are falling away is because they never developed a firm, solid foundation in Christ. One must investigate one's beliefs, test it, try it, before the foundation can be set. Anything less and the foundation's set merely in sand, not bedrock.
Similarly, we must all choose our choice of building materials. Are we building with whims, passions, and concessions or with discipline, self control, and wisdom? Whims are hollow; discipline is solid. Passions are untreated; self-control is cured. Concessions are soft and porous; wisdom, true wisdom, is unyielding and without holes.
Of course, faulty materials are often packaged and sold as their superior counterparts, so one must pay careful to the source of one's character. The Bible calls these materials the "fruit of the Spirit". As Christians, we need to be looking to God for these materials, not to ourselves as we humans are flawed by our own sin, making anything of our production faulty, but God, by very definition being perfection, is able to provide perfect, flawless materials.
It's funny. Solomon wrote just that:
"Trust in the Lord with all your heart. Lean not on your own understanding. In all your ways acknowledge Him and He will make your paths straight." - Proverbs 3:5-6