First of all the matrix is based on the idea that reality is just an illusion. The matrix is a reference to Chang Tsu that say the Matrix is the reality from which the illusion of the world is created.
So first of all the Matrix is the truth and the illusionary world is built on top of that. Like the create Taoist sages Neo is able to look through the illusion of the world and see the matrix, the code that builds the illusion allowing him to do great things.
1. The world of 1999 is the illusion.
2. They go into the matrix to find and free people in the matrix. They also interact with certain people in the matrix such as the oracle.
Also when they are in the matrix they are capable of doing cool kung fu, which is the whole point of the movie, lots of cool kung fu (the pitch for the movie was done by showing japanese animation movies to studio executives and telling them they want to do it with live action)
3. The machines use humans as a power source. They need to keep humans alive and to do that they must create an illusionary world for them to live in, what they call the matrix.
4. As Morpheus said "How do you know what is real?"". We think that the matrix is real because it is a clever simulation. We have no idea that we are living in the dream. Back to Chang Tsu, he once had a dream he was a butterfly and during the dream he completely forgot about the fact he was a man. When we woke he remembered the dream and wondered if he had dreamed that he was butterfly or was he a butterfly now dreaming that he was a man.
People get out of the matrix by being giving a computer virus that "the pill" that causes their connection to the matrix to have problems. This allows them to be traced, but also breaks the connection to the matrix and wakes them up. They don't get out of the matrix, they are out already, they are just unplugged.
There are several liberties in the story and some things that don't really make that much sense but look cool. But overall it is a philosophically based story where Neo is basically a person who goes from uber geek to superhero Buddha.