Horizontally means in a flat, level line — like the floor, or the line where the sea meets the sky — not standing up. You lay a book horizontally on the table; you move horizontally when you slide sideways. Builders, maths teachers, and people giving directions use it: drill horizontally into the wall; the bar lies horizontally across the posts. Its partner is vertically, which is up and down. Though actually, offices also use it about people, not only about lines: to share news horizontally is to pass it to people at the same level, not up to the boss. That is a stretch from the picture of a level line, and it is a little more formal. The home picture is still flat and level.