Integrity, according to the wikipedia definition, is the quality of being honest and having strong moral principles. Its known as the state of being whole and divided. People will claim to have full integrity, but when it comes to the moment to really display it, it will not be seen/riddled with excuses. Most people tend to get 'saying what you mean' mixed up with the actual meaning of 'integrity'.
Saying what you think isn't enough. Actions associated with integrity will be expressed with big honesty. It is far more authentic and it is practiced every day of your life. Little honesty, or saying what you mean, does not come with actions. It will come with word based justifications. For example, someone can shower you with affection, warmth and praise. You then believe this person cares for you/likes you. Then a few days later, they will say something is wrong and be very skepitical about what they are saying, but will claim 'honesty'. Sure feeling change, but its people who practice integrity that are secure enough to know how they feel, know what they want and to be honest from the start. It's a start to say what you mean, but then there is dishonesty about denials and not admitting something not only to yourself, but to others around you. The first integrity practice is admitting things to yourself.
Another thing attached to integrity is having real values. Values are what you think most people should have, regardless of their circumstances. It's ultimately what you think everyone should have in order to live a better and enriching life. Integrity is also having concern about certain values. For example, I believe everyone should display compassion and empathy. I think everyone should consider others, regardless of what happened in that event. Thats having strong values. That is what I think people should have and people should practice to form better lives for everyone around them.
It's wanting every human being to have what others have. One of my biggest values is protecting people, any person, who matches up with my morals. It's displaying compassion even when people have hurt me. Its still going that extra step of care to show people that people can still love and forgive. Everyone makes mistakes. You care about people's safety when they are sick, you show that extra length of care by sending that message and asking if someone is okay. That is the practice of integrity and that is what an authentic, genuine person would do.
No one is above or behind someone else. No one is a 'better' person. Everyone has the capacity to practice integrity until you truly discover your own. Once you practice integrity, your life will have more purpose and meaning. Your relationships will become more stable. You will feel more at ease knowing you are being true to yourself as well as others. Its important to not forget about everyone around you. The more you open up to others around you and put in place your strong morals and values, the more you will feel whole. That is the practice of integrity.