A rocket is a vertical launched craft. Usually it uses rocket engines to propel it forward and doesn't utilise the lift of wings or winglets. If any it only uses control surfaces to help steering in an atmosphere. The main purpose of a rocket is to reach space and an orbit or at least a sub-orbital flight.
With various stages rockets can dump dry mass and get more efficient, while a plane usually doesn't stage. As they don't use lift to maintain altitude, the rocket engines need to counteract the gravity. To determine if the rocket can lift of, the thrust-to-weight ratio can be determined. If the ratio is above one, the thrust generated by the engines is higher than the gravitational force and thus the rocket starts lifting off. Because the engines drain fuel, the craft gets lighter so the ratio also increases with the flight.
Because rockets don't need lift surface, they work in every environment and don't need an atmosphere. But on the other hand rocket engines with sufficient thrust are far more inefficient than jet engines with similar thrust.
The usual flight profile starts on the launch pad on Kerbin. Prior to lift off the jet engines, if any, need to be started to run at full throttle on lift up. When the jet engines are running on full power, the lift off can be initiated with starting the rocket engines and releasing the TT18-A Launch Stability Enhancers.
The rocket then starts to rise and continues so until reaching about 10 km. At this point the gravity turn is initiated by tilting to the east usually. Depending on the targeted inclination the direction of tilting might be different. For example retrograde orbits, where the crafts rotates in the other direction than the body beneath it, the tilt would be to the west. With the gravity turn the craft starts to pick up horizontal velocity which is crucial for an stable orbit. The engines continuing to accelerate the vessel to raise the apoapsis and periapsis out of the atmosphere.
As soon as the apoapsis and periapsis are outside the atmosphere, the craft won't fall back and reached a so called parking orbit. From this orbit it is possible with orbital maneuvers like the Hohmann transfer, to change the orbital shape.