The following definition is taken from $\textit{Theory of Categories}$ by Barry Mitchell
Definition: For $f:B\rightarrow D$ in the category $C$, let
$$(1)\quad \begin{array}{ccccccccc} K & \xrightarrow{a} & B\\ {b}\big\downarrow & & \big\downarrow{f} & \\ B & \xrightarrow{f} & D \end{array}$$
be a pullback. The pair $(a,b)$ is called a $\textit{kernel pair}$ of $f$. A pair of morphisms $a,b:D\rightarrow B$ is called a kernel pair if it is a kernel pair for a suitable $f$. Cokernel pairs are defined dually.
Question: I would like to know what the last sentence: "A pair of morphisms $a,b:D\rightarrow B$ is called a kernel pair if it is a kernel pair for a suitable $f$" mean. What does it mean by a suitable $f$?
Thank you in advance