It's not just metals that tend towards a lower energy state. Most things in an isolated system obey the second law of thermodynamics, which basically states that the entropy of the universe never decreases. This means that entropy is always maximized, which in turn means that energy is always minimized (this relationship can be derived from the first law of thermodynamics). Why is entropy maximized in an isolated system?

Let's look at the equation for entropy:
"S = -k Log(omega)"
where S is the entropy, k is Boltzmann's constant, and omega is the "density of states" or basically the number of "microstates" available to a system.

A microstate is any possible arrangement of the microscopic degrees of freedom in a system, such as the particle positions or the momenta of the particles. It turns out that more microstates are available where certain values of the energy, volume, and number of particles are adhered to by the system: let's call them E*, V*, and N* where the number of microstates is maximized (let's call it omega*). Since there are more microstates available at E*, V*, and N*, the system is more likely to be at E*, V*, and N*.

If that doesn't make sense, think about having a bag of 10 marbles, 9 black and 1 white. You're more likely to pick a black one than a white one, right? Well if omega* is larger than other omega's, then omega* is where the system is more likely to be. When we maximize omega, the number of microstates, we are maximizing the entropy, since the logarithm of a large number is larger than the logarithm of a small number (if you don't believe me, type log(100000) into your calculator, and compare the result to log(10), for example).

Now remember, when we maximize entropy, this corresponds to minimizing energy. So at the heart of things, it's a matter of the system existing at the values of E, V, and N that maximize the number of microstates and entropy. This in turn happens to be where the system is most "stable" in the sense that this is where the system tends to evolve toward. I hope that helps.

Great question! When metal atoms absorb an electron, photon, or other particle with energy, they become excited. You can think about this as the metal atom becoming very agitated and vibrates quickly, disturbing its neighbor atoms. Because of this excess energy, the nearby atoms want to equilibrate with this excited atom, and so the metal atom transfers its energy through to the neighbors and itself is now lowered in energy (returning to a more stable state). This process of transferring excess energy throughout the metal is attributed to the increase in temperature of the metal. Other ways for the atom to return to stable state is to give off energy in the form of radiation (i.e. light or heat). This is why metals seem to “glow” when they are heated at a very high temperature.

This is not just true of metals. In fact every system wants to minimize its total internal energy and dissipate the extra energy into its surroundings because of the second law of thermodynamics. In the case of an atom, the electromagnetic force is pulling the electrons towards the nucleus, so the further away the electrons from the nucleus, the greater the potential energy of the atom. But there are only certain orbitals (or quantum states) that electrons can occupy, and they can't occupy the same orbital (this is called the Pauli exclusion principle). So for a given number of electrons, the most stable atomic state is to fill in the orbitals starting from the lowest energy one. If an electron is excited to a higher energy orbital, it will want to quickly go back to a lower available one. Also, for metals specifically, since they typically have one or two electrons in the outermost shell, if they lose an electron or two they will have lower energy (classically an empty or full shell is lower energy than partially full). Thus they like to form ionic bonds in which they lose electrons.

Source:
1) http://en.wikipedia.org/wiki/Excited_state
2) http://en.wikipedia.org/wiki/Ionic_bond

This is called the second law of thermodynamics: any system will move from a more ordered state to a less ordered state. By moving to a lower energy state, the potential energy that was stored in the metal is released to become kinetic energy. Kinetic energy is less ordered than potential energy, and so is favored by thermodynamics.

All systems "want" to be in their lowest energy configuration. Take for example a ball on a hill. A ball on a hill will roll down the hill until it reaches the bottom of the hill. In the process, the ball is reducing its potential energy (Eg=m*g*h where m=mass of the ball, h=height, and g=the gravitational acceleration). Systems respond to gradients in potential energy be they chemical, gravitational, electrical, or etc. Such gradients produce forces and these forces drive changes in the system. In the example above, there is a gravitational force on the ball due to the change in gravitational potential energy with height (gradient in gravitational energy). If there is no net force acting on a system, then the systems configuration will not change. Such occurrences can be stable, metastable, or unstable. Picture a pendulum balance precariously straight up. The net for will be zero (the gravitational force is balance exactly by the support holding the pendulum up), but as we know, this situation is not stable. Any small variation or perturbation in the pendulum about its current position will result in a net force away from that position. This is the definition of an unstable equilibrium position (i.e. the net force is zero, but any perturbation will cause the system to move away for this point). A stable equilibrium position is when the net force on the system is zero, and any small perturbation about the systems position will result in a force which moves the system back towards the equilibrium position. Picture here the pendulum at rest at the bottom of its swing-any small perturbation about this position will result in the pendulum swinging back down towards the equilibrium position at the bottom of the swing. The metastable equilibrium is like the stable equilibrium in that small perturbations will return the system to the metastable state; however, sufficiently large perturbations will result in the system moving out to another metastable or stable state. Picture here a ball in a hole on the side of a hill. If the ball rolls around in the hole it is stuck (held in the metastable state); however, given enough energy, the ball could be kick out of the hole and would then roll farther down the hill. In summary, systems respond to forces which are the results of gradients in some potential energy function. The forces act to move the system to lower energy states. The state of a system can be classified as stable, unstable, or metastable depending on the effect that variations around that point have on the evolution of the system.

Everything in nature will try to achieve the most stable state, which we define as the state with the least "free energy." Free energy is energy that can do work. For example, water flows downhill to minimize its gravitational energy, salts dissolve in water to maximize their entropy (entropy is a measure of how many ways something can exist, and can be thought of as a measure of randomness or disorder. Something that is more disordered has less energy.), air currents flow and mix to maximize their entropy, wood and other fuels burn to minimize their chemical energy, batteries discharge to minimize their chemical energy. It's not that these things "want" to be stable, it's just that these processes will happen because there is free energy to do something (for example, to burn, or to flow downhill), and once that happens, the system is trapped in a new, lower energy state. (Until it can do something to lower its energy even further.)