pressure
Pressure measures how concentrated a push is, that is, how much force is spread over how much area. This is why a sharp knife cuts easily while a blunt one does not, and why lying on a bed of nails can be survivable while standing on a single nail is not: the same push feels very different depending on the area it acts over. Pressure answers the question of how hard a surface is being squeezed at each spot.
Precisely, pressure is the perpendicular (normal) force pressing on a surface divided by the area of that surface: P = F / A, where F is the force at right angles to the surface and A is the area. Its SI unit is the pascal (Pa), and one pascal equals one newton per square metre (1 Pa = 1 N/m^2). A remarkable fact about a fluid is that, at any single point inside it, the pressure pushes equally hard in every direction, not just downward. Pressure is a scalar: it has a size but no single direction of its own.
Pressure runs through the whole of fluid mechanics: the deeper you dive the more the water squeezes you, a pumped-up tyre holds its shape, and the atmosphere presses on everything at once. One common misconception is to picture pressure as a force. It is not; it is force per unit area. A gentle push over a wide area can give the same pressure as a hard push over a tiny one, which is exactly why snowshoes stop you sinking into snow.
A person weighing 700 N standing on two feet of total area 0.03 m^2 presses on the floor with pressure P = F / A = 700 / 0.03 ≈ 23 000 Pa. Balance on one narrow heel of area 0.001 m^2 and the pressure jumps to 700 000 Pa, which is why heels dent soft floors.
Same weight, smaller area, far greater pressure: pressure is force divided by area.
Pressure is not a force; it is force per unit area, and in a fluid at a point it acts equally in all directions rather than pointing one way.