I'll get you started.
Thrust is indeed the lifting force of the motor. It applies force to the rocket body in opposition to gravity, which is also a force. Obviously, in order to leave the ground, the motor needs to apply more upward force than gravity is applying downward force.
If you were throwing a rocket into the air, then think of thrust as "how strong is your arm?"
A rocket motor's thrust is determined primarily by the chemicals used to create the propellant, the size and location of the propellant grain core, and the size and shape of the nozzle.
Thrust is a key factor in knowing how much weight your motor can lift. If you use the arm example, then obviously a full grown man could apply more thrust than a toddler. Thrust likewise is a key factor in how fast your rocket will be going when the force is applied.
Motor burn length is not a determiner of thrust. If you have an underthrusted motor, it doesn't matter how long it burns -- it's not going to lift the rocket.
But provided you have enough thrust to lift the rocket, then burn time determines how high it will go. That is total impulse. Back to the arms, a grown man could get a good, long wind-up, applying his arm strength over a nice arc. So, two men with the same arm strength, but one with long arms and one with short arms, will throw the rocket different distances. The long-armed one will be able to apply his arm strength for a longer period of time.
However, thrust is often not uniform throughout the burn. Some motors will give you a lot of thrust at ignition, then quickly peter out. Others will burn slowly on the pad, then gain thrust as the rocket continues upward.
All that being said, your best friend for understanding this is
ThrustCurve.org. Put in your rocket's dimensions and weight, then run sims to determine which motors are effective for your rocket, and how high you might expect them to go. Give it a look and come back with questions.