These are the finite difference equations that relate heads at a cell to surrounding heads.

If we solve for the future head (head at next time step) at a given cell, using the current heads at the surrounding cells, we call this explicit or forward difference and we can solve one equation to determine the future head at that cell, because there is only one unknown.

If we solve for the future head (head at next time step) at a given cell, using the future heads at the surrounding cells, we call this implicit or backward difference and we must solve simultaneous equations to determine the future head at that cell, because there are numerous unknowns.

An alternative answer:

On page
http://www.mines.edu/~epoeter/583/06/discussion/basis_of_fd.htm

eqtn 8 is the fundamental finite difference equation

having this we have 2 choices:

we can set n = t, the present time at the beginning of the time step, and solve each equation independently for the heads at i-1 i i+1 (we call this explicit, or forward difference because we use the past heads to solve for future heads)

OR

we can set n = t+^t, the future time at the end of the time step, and solve the equations (3 in the case of a 1D problem) simultaneously for the heads at i-1 i i+1 (we call this implicit, or backward difference because we use the future heads to solve for future heads ... this requires simultaneous solution because we do not know the future heads)