Well, Neo is the Anomaly. If you're really good with mathematics (as I am), the first thing you figure out is that a Matrix, or several matrices, is a mathematical term. A matrix is some compination of many equations with mutliple variables.
[9 -7] [x] [result a]
[3 11] [y] [result b]
[8 2] [z] [result c]
I'm not saying this matrix is correct at all, but it shows atleast just about what a matrix is (I'm still in the process of learning this very wicked way of solving equations with mutliple variables).
Back on topic, the Matrix is a colleciton of billions of matrices, each containing another nine-hundred billion equations, the codes you see all around, the programs, etc, etc.....
However, this Matrix that the architect designed (he must be The One in mathematics) is flawed, because there is an equation, an Anomaly, that created unbalance in the Matrix, it can alter the entire system.
This Anomaly is Neo.
Smith is Neo, but also his Negative. With other words, Smith is that which tries to balance out the Anomaly.
Thus, when Smith takes over Neo, his opposite, this equation that tries to balance out the Anomaly does so, and what happens when they balance eachother out?
They return to the value of 0 (ZERO, NIL, or whatever you might call it). It's simple to explain:
Neo is the Anomaly. Smith is that which tries to balance out this Equation. Both are independant of the Matrix, not part of it, so when Smith assimilates Neo, they cancel eachother out. If you know maths, you understand this.