The column space of a matrix A is the vector space spanned by the columns of A. The dimension of the column space is equal to that of the row space, which in turn is equal to the rank of A.
For instance, the matrix,
[ 1 1 2 ]
[ 2 2 4 ]
[ 3 5 6 ]
Performing elimination will show that this matrix has two pivot variables and one free variable, and thus the column space spans a two dimensional subspace of R3. It is also plainly visible, as the third column is a direct multiple of the first column, and is thus dependent.