Newton's second law states that if the net force is not equal to 0, the object will accelerate in the direction of the motion.
Acceleration is directly proportional to force and INVERSELY proportional to mass. In other words, if the force increases and the mass is the same, the acceleration will be greater. If the mass increases and the force stays the same, the acceleration will decrease. To make it easier, think of a person trying to push a very big rock that is heavy and a person pushing a small rock the size of their palm.