Newtons second law says that the net force of an object is is equal to the time rate of change of its linear momentum.
in other words force is the time derivative of momentum. Momentum is mass*velocity. since this only applies to objects with constant mass, in the equation mass can be considered a constant and pulled out
so you end up with F=m(dv/dt).
since acceleration is the time derivative of velocity this works out to
this is the most famous form of his second law and clearly shows that F is directly proportional to a. for example if mass is constant and you double the force, you will double the acceleration.
net force is the total amount of things working on an object. if your acceleration is 0, the net force is 0 because the amount you have doing work on the object is the exact same amount acting against it ie. the force of a guy pushing a box at a constant speed is going to equal the amount of frictional force in the opposite direction.
if the thing starts to accelerate, it is because the forces acting on the object are imbalanced, causing its velocity to change.
the guy will start pushing harder on the box to speed it up, he needs to push harder than the amount of frictional force going in the opposite direction hes pushing.
maybe disregard that last examlple it makes it more confusing