Morpheus: What is the Matrix? Control. The Matrix is a computer-generated dream world built to keep us under control in order to change a human being into this.
[holds up a Duracell battery]
Neo: No, I don't believe it. It's not possible.
Morpheus: I didn't say it would be easy, Neo. I just said it would be the truth.

Trinity: I know why you're here, Neo. I know what you've been doing... why you hardly sleep, why you live alone, and why night after night, you sit by your computer. You're looking for him. I know because I was once looking for the same thing. And when he found me, he told me I wasn't really looking for him. I was looking for an answer. It's the question that drives us, Neo. It's the question that brought you here. You know the question, just as I did.
Neo: What is the Matrix?
Trinity: The answer is out there, Neo, and it's looking for you, and it will find you if you want it to.

The digital pimp hard at work.

Switch

Agent Brown: What were you doing?
Agent Jones: He doesn't know.

If real is what you can feel, smell, taste and see, then 'real' is simply electrical signals interpreted by your brain

Morpheus

What are you waiting for? You're faster than this. Don't think you are, know you are. Come on. Stop trying to hit me and hit me.

Morpheus

Neo: I thought it wasn't real
Morpheus: Your mind makes it real
Neo: If you're killed in the matrix, you die here?
Morpheus: The body cannot live without the mind

Unfortunately, no one can be told what the Matrix is. You have to see it for yourself.

Morpheus

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The Matrix Quotes

I'd like to share a revelation that I've had during my time here. It came to me when I tried to classify your species and I realized that you're not actually mammals. Every mammal on this planet instinctively develops a natural equilibrium with the surrounding environment but you humans do not. You move to an area and you multiply and multiply until every natural resource is consumed and the only way you can survive is to spread to another area. There is another organism on this planet that follows the same pattern. Do you know what it is? A virus. Human beings are a disease, a cancer of this planet. You're a plague and we are the cure.

Agent Smith

Neo: What are you trying to tell me? That I can dodge bullets?
Morpheus: No, Neo. I'm trying to tell you that when you're ready, you won't have to.