What is the meaning of "comparable Dirac and Majorana terms"?

Your reference is just fine and clear, and refers you to [2] and [20] if you wish to know more. It discusses its mass matrix (1) mixing active and sterile species.

If $m_D=0$, or $m_M=0$, there is no mixing. If $m_Dll m_M$ as in the celebrated see-saw scenario, the masses of the eigenstates are huge ($m_M$) and small ($m_D^2/m_M$), respectively, but then the mixing is insignificant, $O(m_D/m_M)$; this is what the author is reminding your to exclude.

So in order to have nontrivial sterile neutrinos that matter (~are observable, indirectly: second class oscillations), you need comparable mass matrix parameters $m_D$ and $m_M$, i.e. they are comparable numbers, like 1 and 3.7 times a common mass scale. That mass scale must, of course, be small, since we are talking about neutrino masses, and we know active neutrino masses are small.