Gaslighting is a form of mental and emotional manipulation. Someone who is gaslighting you will call reality into question in order to make you question your own memories and/or perceptions. They may tell you they didn't say what you heard them say, they didn't do what you saw them do. They will tell blatant lies, denying an event which you witnessed, "That didn't happen". They will deny doing something which you have proof they did, "I never sent that email", yet you are looking at that email on your phone. They will contradict your opinions and emotions, "You aren't angry. You're happy that happened." They will attack your emotions, thoughts, and behavior insinuating there is something wrong with you, "You always overreact", "Why are you so hypersensitive?" When you confront them about something, they will attack your character and your credibility, "Why do you make these things up?" They will deny reality, "You don'to have bipolar disorder. There's no such thing." (There is.)
The point of gaslighting is to make you question yourself, your sanity. It is, literally, crazy-making. The term gaslighting originates from a film from the 1940s "Gas Light", where a husband tries to convince his wife and the people around her that she is insane so he can collect her inheritance. He does this by manipulating things in her environment (i.e. adjusting the gas lights) then insinuating there is something wrong with her when she notices they have been changed.
It is used for the same purpose in the current era, to make you doubt yourself.
Who does it?
Usually narcissists and antisocials (psychopaths/sociopaths).
Why do they do it?
It's usually an attempt to take attention away from their own pathology and convince you that the problem is yours, not theirs.
What kind of damage does it cause?
It can make you doubt yourself. You may find it hard to make decisions and have trouble trusting your own five senses. You may even start to believe their spin, that there is something wrong with you and they are perfectly normal.
What can you do about it?
Get away from it. Seriously. If someone close to you is doing this to you, they don't truly care about. They are clearly willing to sacrifice your well-being so they can be right. That's not love, that's abuse.