What does this equation mean?

The multiplication step follows directly from two textbook circuit laws. Apply a voltage $V_i$ simultaneously to each row i, representing the i-th component of an input vector. By Ohm’s law, the cell at row i and column j draws a current $V_i$ times its conductance $G_i$j. By Kirchhoff’s current law, every current flowing into a given column sums automatically on that column’s wire, so the total current collected at the bottom of column j is $I_j = \sum_i V_i\, G_{ij}$. which is precisely the j-th component of the matrix-vector product between the input vector and the conductance matrix stored across the array — computed in one step, in parallel across every cell, using nothing but the physics of the wires and the stored conductances rather than a clocked multiply-accumulate circuit stepping through the same product one term at a time [ 6 ] . Because the weight is stored and multiplied in the same physical cell, it never has to be fetched from anywhere else to be used — the specific and narrow sense in which this design avoids the von Neumann bottleneck, distinct from the neuromorphic case above, which brings memory near to compute per core but still executes each multiplication as a discrete digital step.