What exactly is work? What exactly is work? My book confuses me:

a force can lift an object to a height h, or it can accelerate an object through gravity. In all these cases, a force displaces an object and change the object's total energy.

The examples it gives confuse me. On one hand, there is lifting and on, accelerating through gravity. 
I can imagine how lifting will change total energy (kinetic + potential). It essentially gives it more potential energy, and does not take from it any kinetic energy. But just dropping an object and let gravity do the work does not seem to me to increase total energy. Because the total amounts of kinetic and potential energy should be equal.  If just let drop, the object will gain kinetic and lose some potential. Not really anything added to the total energy.
 A: Work is transfer of energy from one system to another OR transformation of energy from one form to another.  Either way, work does not create energy.
When I lift an object, I am transferring energy from my body/muscles to the object-earth system.  The energy goes into potential energy of the object-earth system because the separation between the object and the earth increases.
When I drop an object, the energy stays in the object-earth system, but is transformed from potential energy to kinetic energy.  The gravitational force does the work, i.e. produces the transformation of energy from one form to the other.
A: You're completely correct, letting an object fall under the influence of gravity will not change its kinetic+potential energy, it just transforms potential energy into kinetic energy, while leaving the total constant.
However, OTHER forces could cause the kinetic energy to increase without changing the potential energy. Imagine a flat ice rink, and a puck sitting in the middle of it. Initially, the puck has zero kinetic energy, and some potential energy depending on how high up your ice rink is. Then you whack it with a stick, and it goes sliding off! The puck is still at the same height, but now it has kinetic energy: the force (hitting it with a hockey stick) caused it to gain energy.
Force could also cause the puck to LOSE kinetic energy. For example, if the puck is sliding towards a goal and a goalie stops it, the force on the puck has SLOWED THE PUCK DOWN, thus decreasing its kinetic energy.
A: Work is defined as $\displaystyle\int F(d) \cdot d$ where $F(d)$ is the net force acting on the object. That's it, that's the definition. 
You might ask; why do scientists talk about energy and work so much? The answer is that experimental science shows that the energy in a system is constant, and thus energy is a useful concept which can be talked about in a meaningful sense.
A: Work is transfere of any type of energy into kinetical energy. 
$$
T=\frac{mv^2}{2}
$$
where $v$ is the velocity of the particle in some referential frame and $m$ is the mass of the body.
When the body is lifted in a gravitational field a force $F$ is required to balance the gravitational force $F_g$. During the lift, the force $F_1$ are doing a positive work $W_{F_1}=|W_{F_1}|$ and gravity are doing a negative work $W_{F_g}=-|W_{F_g}|$. At any instant of time, the kinematic energy of the body is equal to (assuming that the body are taken from rest):
$$
T = \Delta T _{1}= W_{F_1} + W_{F_g} = |W_{F_1}| -|W_{F_g}|
$$
Then, during the lifting, the work done by the force $F$ need to be greater than graviational work. When you finish the lifting, the boddy is stoped, and this is an acceleration so we need a force to do that. Now a force $F_2$ is need to stop the body. This force make a work as well, need to enrase the kinetic energy:
$$
W_{F_2} = \Delta T _{2} = - \Delta T_{1} = -|W_{F_1}| + |W_{F_g}|
$$
then 
$$
W_{F_1} + W_{F_2} = - W_{F_g}
$$
This means, the work done by $F_1$ and $F_2$ is equal to the the negative of work done by gravity. By conservation of energy, the work done by gravity is equal the energy taked from the gravitational field. 
$$
\Delta E_{g} =  W_{F_1} + W_{F_2}
$$
A: Work is a definition of the expenditure of energy over time. 
That's it.  
It's not contained in the definition of any other physical quantity.  One could make lots of examples that generate work with chemical reactions (internal combustion engines, explosives), mechanical dynamics (piston firing), electromechanical transformation (electric motor), and so on. Even potential energy in a gravity field like the height of a mass over the centre of the earth.
You are confusing closed system energy. Your closed system would NOT increase or decrease energy. It would transform from one to another form.   What that poorly written book passage is saying I believe is that the total POTENTIAL energy changes by converting to other forms like kinetic (motion) and others like mechanical energy( sound waves emitted) and so on. Anything else is breaking the first law of thermodynamics. Energy is conserved and cannot be created nor destroyed.
