The contour matrix that contourc returns is basically a bunch of vertices that define the contour lines. Each vertex is an (x,y) pair and they are stored as columns in the contour matrix:
x1 x2 x3 ...
y1 y2 y3 ...
Except, there are also some columns in the matrix that hold information about how many vertices the contour line has and level (e.g. 0.8) of the contour. So the contour matrix might actually look something like this:
0.8 x1 x2 x3 ...
386 y1 y2 y3
The first column says that the next 386 columns are going to contain coordinates of a line at the contour level 0.8.
This documentation section explains the structure of the matrix in a little more detail.
