There are multiple conservation laws in nature meaning these are considered to be scientific truths which are fundamental and foundational to all modern science as we know it.

Perhaps the most familiar or common conservation law in science is that of the conservation of energy.

What this means is that energy can neither be created nor destroyed, only changed from one form to another. There are many different types of energy which can be converted back from one form to another. Most energy is in the form of potential and kinetic energy.  Examples of potential energy are weights lifted to some height or opposite charges separated by a distance. When materials are raised to a height, they can do work when they fall to a lower level such as water flowing over a water wheel or the weights in a grandfather clock turning its hands to keep and tell time. 

A common example of potential energy is the separation of opposite charges. This can be in the form of an electronic capacitor. When a charged capacitor discharges, it can do electrical work such as turning a motor or lighting a sign. A similar but more complicated example of charge separation is that of chemical potential energy where a chemical reaction can do work such as in a common household battery for a toy. Other forms of chemical potential energy can be found in glow sticks or even dynamite. Kinetic energy is the energy of motion. 

The energy a moving car has when coasting along at some speed is kinetic energy and this is due to both its mass and velocity. Energy is commonly measured in units of Watts, sometimes in kiloWatts. The law of conservation of energy states that you can convert any one type of of energy into another kind of energy. In other words, a Watt from a batteries chemical potential energy could be converted into a Watt of kinetic energy in a toy car.

Similarly the chemical potential energy in rockets fuel can be converted into kinetic energy of a launched rocket. 

A more familiar example would be the chemical potential energy in gasoline being converted into the kinetic energy of the engines pistons or the car moving forward. In all of these conversions, there is some loss to useless waste heat such as that from friction. 

Multiple forms can be combined into a single process. Lifting a bar magnet gives it potential energy. Allowing it to drop converts this potential energy into kinetic energy. If this moving magnet passes through a circuit of copper coils , this kinetic energy will be partially converted into electrical energy. The electricity created in this generator can then be used to run a motor, turn on a light or even to initiate a chemical reaction. 

So all these forms of energy can be converted into other forms of energy. A very important concept to be included with a discussion on the law of conservation of energy is the 2nd law of thermodynamics. Here, the law of nature is that in converting heat energy into another form of energy, there will always be some loss of energy as useless lower temperature heat. In other words, no conversion of energy will be 100% efficient, there will always be some loss of energy as heat when doing useful work. If no work is done, then under limited (frictionless) conditions a full conversion for a limited period of time is possible. 

Examples of this heat loss in an energy conversion is the exhaust from either your car or your local electrical power plant. Even if you were to increase the overall efficiency of a fossil fired electrical utility by using some of the waste heat in an industrial process, the efficiency is functionally limited by the relative difference in operating temperatures and is never 100%. 
Electrical lines lose energy through heating losses in the circuits. Mechanical systems lose energy in heating components due to friction. Objects moving through air lose energy when causing turbulence and moving/pushing the air around due to their motion resulting in slightly heating the air. 

One rather little known fact about the law of conservation of energy is that this law is equivalent to saying that time is symmetric when reversed. A full understanding of this requires advanced physics and it does assume there are no energy losses during the process (such as heating or an increase in disorder). 

It is only when including the useless heat energy lost in converting one form of energy into another that the true nature of energy is realized to be a conserved quantity. You always have the same amount of energy before and after any time or process. The energy is simply converted into one or more different forms through any sequence of operations or events.