Static Friction
The frictional force experienced by an object on a solid surface is called static friction. At first it's exactly equal in magnitude and opposite in direction to the force you exert on the object. As you push harder, static friction pushes harder back --- until the force you exert reaches the threshold of motion, at which point the object begins to move. If the surface is horizontal, you can estimate the threshold using the following equation: maximum force of static friction = weight of the object x coefficient of friction.
Coefficient
The coefficient of static friction is a constant that varies for different objects and surfaces. If you've ever tried to push a heavy box across a floor, for example, you probably know it's much easier to push it across smooth marble than rough concrete. That means the coefficient of static friction for the box on the marble surface is lower than the coefficient for the box on the rough concrete, because a bigger coefficient means more static friction.
Weight
This equation also tells you that maximum static friction on a horizontal surface increases with weight --- the force exerted on the object by Earth's gravity. You'll get much less friction pushing an empty suitcase than you would if you were pushing an empty freight train. The more an object weighs, the greater the threshold of motion and the harder you'll need to push to get it going.
Kinetic Friction
Once an object is sliding, the force of friction on it is given by a different equation: weight of object x coefficient of kinetic friction. The coefficient of kinetic friction is typically less than the coefficient of static friction. What this means in practical terms is that once an object is sliding, the force of friction on it decreases, so it's easier to keep an object moving once it's already in motion.