The obvious case is that of a random walker on a one-, or two- or three-dimensional lattice (dubbed coordinate space hereafter).
Consider a system whose energy is defined by the orientation of single spins. Consider the state \( i \), with given energy \( E_i \) represented by the following \( N \) spins $$ \begin{array}{cccccccccc} \uparrow&\uparrow&\uparrow&\dots&\uparrow&\downarrow&\uparrow&\dots&\uparrow&\downarrow\\ 1&2&3&\dots& k-1&k&k+1&\dots&N-1&N\end{array} $$ We may be interested in the transition with one single spinflip to a new state \( j \) with energy \( E_j \) $$ \begin{array}{cccccccccc} \uparrow&\uparrow&\uparrow&\dots&\uparrow&\uparrow&\uparrow&\dots&\uparrow&\downarrow\\ 1&2&3&\dots& k-1&k&k+1&\dots&N-1&N\end{array} $$ This change from one microstate \( i \) (or spin configuration) to another microstate \( j \) is the configuration space analogue to a random walk on a lattice. Instead of jumping from one place to another in space, we 'jump' from one microstate to another.