Throughstones connect one side of the wall to the other as this picture taken from above a wall I built recently shows. The idea is that they tie together both halves of the wall and thus make the whole wall stronger. The use of 'truffers' as it is pronounced in this part of Yorkshire, near Whitby is important as most of the stone is fairly lumpy.and it is difficult to get stone to overlap from both sides.
When I lived in Ireland the use of throughstones was not always common as the stone was often irregular and/or thinner and it was a matter of course that both sides of the wall ended up with overlapping stones making the use of 'truffers' unnecessary.