What does this notation mean, concerning a vector?
I suspect, given the context, that this notation is for the expected value. So $\langle\xi(t)\rangle=0$ would mean that $\xi(t)$ is zero mean, all of the entries of the vector are zero mean.
As was suggested as an additional clarification by O.spectrum:
$$\langle \xi(t)\rangle = \mathbb E\xi(t) = \begin{pmatrix}\mathbb{E}\xi_1(t)\\\vdots\\\mathbb{E}\xi_m(t)\end{pmatrix} = \boldsymbol{0}_{[m\times 1]}$$