In this statement, I understand that the vectors correspond to the time direction: in a single carrier system, a signal vector X = [x1,x2,...,xn] contains the samples corresponding to time slots 1, 2 , ... n.
In a multicarrier context as OFDM, the frequency and the time are splitted. Thus you can consider the signal as an array
X =
[x11, x12, ...x0n;
x21,x22,...,x2n;
........
xM1,xM2,...xMn],
where the M rows correspond to the M carriers along the frequency axis, and the n rcolumn correspond to n succesive OFDM symbols. It reflect the statement "each carrier carries vector of array".