Local tallies count the difference (between two resulting board positions) of the difference in the number of stones invested by each side (black and white).
For example, given an endgame problem position (P), we consider two positions (P1 and P2) which result when either black plays first (P1) or white plays first (P2).
The single-board tally is simply the count of how many extra stones were played by a given player (positive for black, negative for white) for each board position. In other words, if, in the continuation P1, black plays two stones and white plays one (read: gote for black), then the single-board tally is +1 (positive one).
We make a similar calculation for P2 (gote for white as well, so -1) and then subtract P1-P2 to get the local tally, in this case 1 - - 1 = 1 + 1 = 2.
This makes possible the conversion of deiri (swing) endgame values to miai (true value) endgame values by simply dividing the swing value (value of P1 - value of P2) by the number of stones invested (single-board tally for P1 - single-board tally for P2 = local tally for P ). In this way miai values give you a "return on investment" for a single stone.