Pascal's Principle

Before we get right into Pascal's Principle, it's best to preface certain properties about fluids. There are two main types of fluids: liquids and gases. Both liquids and gases take the shapes and volumes of their containers but they have two main differences when they're under pressure. Liquids are ideally incompressible which means you can't change their volume with ease(this is actually not the case with fluids in real life as you can change their volume slightly but the point still stands that you can't easily change a liquid's volume). The same can't be said for a gas which is a compressible type of fluid, meaning you can alter its volume relatively easily. This is why it's easier to squeeze an empty water bottle(which is filled primarily with gaseous carbon dioxide) than a full one(which is filled with liquid water).

If we had a hydraulic press, like the one below, where we had forces applied on both sides. If I were to push on the liquid, the molecules that I push on would push back all the layers of fluid throughout the liquid until the molecules at the other end get pushed. These molecules would push back on the other piston exerting the same amount of work you applied on your side's piston. This is evident because the energy from you doing work on the piston on the left has to go somewhere since energy is assumed to be conserved. The energy, and thus pressure, gets transmitted throughout the fluid through inelastic collisions in the fluid until we get to the right piston. This piston moves due to the pressure caused right under it. Since the energy must be the same, the total pressure is the same which means many things, especially in hydraulic engineering.