{\displaystyle d\mathbf {F} _{n}=-p\,d\mathbf {A} =-p\,\mathbf {n} \,dA.} The minus sign comes from the convention  that the force is considered towards the surface element, while the normal vector points outward. The equation has meaning in that, for any surface S in contact with the fluid, the total force exerted by the fluid on that surface is the surface integral over S of the right-hand side of the above equation. It is incorrect (although rather usual) to say "the pressure is directed in such or such direction". The pressure, as a scalar, has no direction. The force given by the previous relationship to the quantity has a direction, but the pressure does not. If we change the orientation of the surface element, the direction of the normal force changes accordingly, but the pressure remains the same.Pressure is distributed to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. It is a fundamental parameter in thermodynamics, and it is conjugate to volume. Units
The SI unit for pressure is the pascal (Pa), equal to one newton per square metre (N/m2, or kg·m−1·s−2). This name for the unit was added in 1971; before that, pressure in SI was expressed simply in newtons per square metre. Other units of pressure, such as pounds per square inch (lbf/in2) and bar, are also in common use.
However, the US National Institute of Standards and Technology recommends that, to avoid confusion, any modifiers be instead applied to the quantity being measured rather than the unit of measure. For example, "pg = 100 psi" rather than "p = 100 psig". Differential pressure is expressed in units with "d" appended; this type of measurement is useful when considering sealing performance or whether a valve will open or close. Presently or formerly popular pressure units include the following:

atmosphere (atm)
manometric units:
centimetre, inch, millimetre (torr) and micrometre (mTorr, micron) of mercury,
height of equivalent column of water, including millimetre (mm H2O), centimetre (cm H2O), metre, inch, and foot of water;
imperial and customary units:
kip, short ton-force, long ton-force, pound-force, ounce-force, and poundal per square inch,
short ton-force and long ton-force per square inch,
fsw (feet sea water) used in underwater diving, particularly in connection with diving pressure exposure and decompression;
non-SI metric units:
bar, decibar, millibar,
msw (metres sea water), used in underwater diving, particularly in connection with diving pressure exposure and decompression,
kilogram-force, or kilopond, per square centimetre (technical atmosphere),
gram-force and tonne-force (metric ton-force) per square centimetre,
barye (dyne per square centimetre),
kilogram-force and tonne-force per square metre,
sthene per square metre (pieze). Examples
As an example of varying pressures, a finger can be pressed against a wall without making any lasting impression; however, the same finger pushing a thumbtack can easily damage the wall. Although the force applied to the surface is the same, the thumbtack applies more pressure because the point concentrates that force into a smaller area.