In mathematics a vector is just a one-dimensional series of numbers. If the vector is written horizontally then it is a row vector; if it's written vertically then it's a column vector.

Whether a vector is a row or a column becomes significant usually only if it is to figure in multiplication involving a matrix. A matrix of m rows with n columns, M, can multiply a column vector, c, of m rows, on the left but not on the right.

That is, one can perform Mv but not vM. The opposite would be true for a row vector, v, with 1 row and m columns.