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Pascal's law says pressure applied to a confined fluid is transmitted undiminished, so the same pressure acts on both pistons and force scales with area. 200 N on 0.001 m2 makes 200 kPa, which pushes 4000 N on a 0.02 m2 piston - a twentyfold gain. The large piston moves only a twentieth as far, so work balances.
Pressure transmitted
P = F1 / A1 = F2 / A2
Force multiplication
F2 = F1 x A2 / A1
Because a large area ratio is easy to build in a compact space, and flexible hose lets the output be placed anywhere.
Practically, yes. Trapped air compresses instead of transmitting force, which is why brake systems must be bled.