I am not sure which Matrix you are referring to, but at the same time it sounds like general matrix operations that confuse you, so here's a quick intro to linear algebra:
a matrix is an ordered collection of numbers and in computer graphics it's mostly a 2 dimensional grid with 3x3 or 4x4 entries. Matrices can be multiplied in order to yield a new matrix. This is of particular interest since a coordinate/vector can be regarded as a one-dimensional matrix. Here's how the two get multiplied, assuming a 4x4 matrix and a 4x1 vector (4 rows, 1column):
Code:
Matrix * in-vector = output-vector
(e11 e12 e13 e14) (x) (x*e11 + y*e12 + z*e13 + w*e14)
(e21 e22 e23 e24) (y) (x*e21 + y*e22 + z*e23 + w*e24)
(e31 e32 e33 e34) * (z) = (x*e31 + y*e32 + z*e33 + w*e34)
(e41 e42 e43 e44) (w) (x*e41 + y*e42 + z*e43 + w*e44)
If e11,e22,e33 and e44 are all 1 and the rest of the matrix is 0, you have an Identity Matrix and the resulting vector would simply be (x,y,z,w).
Usually you have an x,y,z coordinate (or U,V,0 for texture coordinates) and w is set to 1. With w==1 looking at the last column of the equation you can see that this basically adds the vector (e14,e24,e34,e44) to the original (x,y,z,1). Therefore (e14,e24,e34,e44) is said to be a translation vector which moves the input point around (or shifts the texture around).
If you have an identity matrix (everything zero accepts for the center diagonal from top left to bottom right) and then change the diagonal to something other then 1, e.g. to all 4s, your output vector changes to (4x, 4y, 4z, 4w).
To summarize: the 4th column (or the 4th row- I don't know which standard the shader uses) determines offset/translation. The diagonal (e11,e22,e33,e44) determines scaling.
What about the rest of the elements ? They rotate your input vectors. e12, e13, etc. are sines and cosines of a rotation. If you want to figure out how to set those- do a google search for "rotation matrix".