In the context of e.g. a [pseudo-orthogonal Lie group](http://en.wikipedia.org/wiki/Indefinite_orthogonal_group)

$$\tag{1} O(p,q)~:=~ \{\Lambda\in {\rm Mat}_{n\times n}(\mathbb{R}) ~|~\Lambda^T\eta\Lambda= \eta  \} $$

of pseudo-orthogonal matrices $\Lambda$ for the metric 

$$\tag{2} \eta_{\mu\nu}~=~{\rm diag} (\underbrace{1,\ldots,1}_{p~\text{times}},\underbrace{-1,\ldots -1}_{q~\text{times}}), \qquad n~=~p+q,$$

a "vector of $O(p,q)$" is an element of the $n$-dimensional _vector representation_ (aka. the _defining representation_ or _fundamental representation)_ of $O(p,q)$.

See also [this](https://physics.stackexchange.com/q/41424/2451) related Phys.SE post.