what is the matrix?

Morpheus: At last... Welcome, Neo. As you no doubt have guessed, am I Morpheus. I imagine that right now you feel a bit like Alice, tumbling down the rabbit hole, hm?
Neo: How can you say that?
Morpheus: I can see it in your eyes. You have the look of a man who accepts what he sees because he is expecting to wake up. Ironically this is not far from the truth. Do you believe in fate, Neo?
Neo: No.
Morpheus: Why not?
Neo: Cause I don't like the idea that I'm not in control of my life.
Morpheus: I know exactly, what you mean. Let me tell you why you're here - You are here because you know something, what you know you can't explain - but you feel it. You felt it your entire life that there is something wrong with the world. You don't know what it is but it is there like a splinter in your mind, driving you mad. It is this feeling that has brought you to me...do you know what I'm talking about?
Neo: The matrix?
Morpheus: Do you want to know, what it is?
Neo: (nodds.)
Morpheus: The matrix is everywhere. It is all around us even now in this very room. You can see it when you look out your window or when you turn on your television. You can feel it when you go to work, when you go to church, when you pay your taxes. It is the world that has been pulled over your eyes to blind you from the truth.
Neo: What truth?
Morpheus: ...That you are a slave, Neo. Like everyone else you were born into bondage, born into a prison that you cannot smell or taste or touch. A prison for your mind...Unfortunately no one can be told what the matrix is. You have to see it for yourself.