Thrust
A rocket engine accelerates propellant to high speed and ejects it. By Newton's third law the rocket gains equal and opposite momentum. Thrust ≈ ṁ·vₑ + (pₑ − pₐ)·Aₑ, where ṁ is the mass flow, vₑ the exhaust speed, and the pressure term accounts for the nozzle exit.
Specific impulse
Specific impulse Isp measures efficiency: the seconds a kilogram of propellant could produce one kilogram-force of thrust. It equals effective exhaust velocity divided by g₀. Kerosene/oxygen engines reach about 300 s in vacuum, hydrogen/oxygen about 450 s, and ion thrusters several thousand seconds — but with tiny thrust.
The rocket equation and staging
Tsiolkovsky's equation Δv = Isp·g₀·ln(m₀/m_f) shows that Δv grows only logarithmically with the mass ratio. Reaching orbit needs roughly 9.4 km/s including losses, which a single stage with realistic structure can barely achieve. Staging drops empty tanks and engines so later stages push less dead mass.