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Each capacitance-matrix element between two conductors is a measure of how much excess charge will be on one conductor when the other is at a 1-v potential and all other conductors are grounded. This is a very specialized condition and gives rise to much confusion.
Suppose you have 5 conductors in parallel and a 1-v potential is placed on conductor 3 and all the other conductors are at 0-v potential. To do this will require placing some extra plus charge on conductor 3 to raise it to a 1-v potential with respect to ground. This plus charge will attract some negative charge to all the other nearby conductors. The negative charge will come out of the ground reservoir to which each other conductor is connected. How much charge is attracted to each of the other conductors is a measure of how much capacitive coupling there is to the conductor with the 1 v applied. Due to the attraction is used the minus sign.
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