There are four forces in nature, gravitational, electromagnetic and two types of nuclear forces.
Gravity is a force two objects exert on each other because of their mass. The magnitude of the force depends on the product of the two masses and it decreases if the two objects move farther apart. Usually the force is small unless at least one of the masses is very large. Two baseballs would exert a very small force on each other even if they were so close that they were touching. However, the earth has a very large mass (6x1024kg) and exerts a noticeable force on a baseball. That force pulls the baseball toward the center of the earth and keeps the baseball from flying away from the earth when you throw it.
The gravitational force the earth exerts on an object is proportional to the mass of that object so the magnitude of the force is written
F = Mg
where g is the constant of proportionality, which depends on the earth's mass and how far you are from the center of the earth. g is usually called the gravitational field (of the earth in this case). It has about the same value everywhere on the earth's surface where g = 9.80m/s2 . Note that the units of g are the same as the units of acceleration.
If gravity is the ONLY force acting on an object of mass M, then the magnitude of its acceleration is a = F/M = Mg/M = g. If gravity is the only force acting on an object we say it is in FREEFALL. So in freefall, all objects will have an acceleration equal to g. That is why some people call g the acceleration due to gravity, but I do not like that expression.
The gravitation force on an object is often called the weight of the object. Thus weight is a force. Since the weight is = Mg and g is roughly constant on the surface of the earth, people often use weight when they should use mass. They say a can of peaches weighs 1kg. Technically it weighs 9.8N, what they mean is that it weighs as much as 1kg weighs. In English Units, the unit of force is a pound. 1pound (1lb) = 4.4N. 1kg weighs 2.2 pounds.
Contact forces occur when objects are touching each other. The first one is a normal force. When I set a book on a table, the table exerts a force on the book to hold it up and keep it from falling through the table. This force is perpendicular to (i.e. normal to) the surface of the table. The atoms in the table are bonded together and push back on the book when it tries to push them apart. When I stand on the floor, it holds me up with a normal force.
Friction always opposes the sliding motion of one surface past another. The force is parallel to the surface. (Remember the normal force is perpendicular to the surface.) In some cases friction is a hindrance, but in other cases it is essential. For instance it is difficult to walk without friction, i.e. on wet ice there is very little friction and it is very hard to walk. When we drive a car, we depend on friction between tires and the road to supply the force necessary to accelerate the car; whether we are speeding up, slowing down or turning.
When I bicycle along, I notice that the faster I go, the harder I have to pedal. The reason is that the air resists my movement through the air. This force is called a drag force or viscous force. If I go faster the force gets larger, it depends on how fast I'm moving relative to the air. (Frictional forces do not usually vary much with speed.) Since it opposes my motion through the air, it is in a direction opposite to my motion through the air. If the air is still and I'm going east, the drag force is toward the west.
If I drop a ball off a tall cliff, it will accelerate as it starts to fall. If gravity were the only force it would continue to increase its speed by 10m/s every second, but it does not. The air resists its motion through the air and the drag force gets larger as the speed increases. When the speed gets large enough this force cancels the gravitational force on the ball so the net force on it is zero and the acceleration is zero, i.e. the velocity, and the speed are constant, This speed where they cancel is called the terminal speed. The terminal speed of an object depends on its density and size. For objects of the same density, the smaller one will have a smaller terminal speed. That is why fog droplets have much smaller terminal than rain drops.
The last 3 forces, normal force, friction and air resistance, are really electric in origin.