All light is made of electromagnetic waves.  This means that like any wave, there is something repeatedly sloshing back and forth with light.  A water wave is crests and troughs on the water going up and down over and over as they travel across the surface.  Light waves have some resemblance in that with light, it is electric and magnetic fields which are periodically wobbling back and forth. 

Light also happens to come in little individual packets of energy known as photons.  Each photon has only a single portion of an electric and magnetic field which vibrate perpendicular to each other.  This means that if the electric field is vibrating up and down as it is coming towards you, then the magnetic field is vibrating left and right.  Most natural light will have this orientation of each photon randomly directed (although the magnetic field of any photon will always be at a right angle to the electric field).

Light is called unpolarized when the fields are randomly organized in different directions in this way.  Sunlight, light bulbs, fire and most light sources emit unpolarized light.  In this sense, most light waves are more like the smaller waves on the ocean or those in a swimming pool with lots of people in it.  There is not a simple circular pattern coming from an isolated source but rather a hodgepodge of lots of these circular patterns coming from many sources all at once.  With light, the electric field of any photon could be at any angle as it travels.  The photon is just as likely to have its electric field going up down as it is to have it going left and right or at any angle for that matter.

Light can be polarized using multiple methods although one very common way this occurs is through reflection.  Due to the interactions of the electric field with the dielectric surface of a mirror or other reflector, reflected waves have higher polarization than the source terms to the reflection.  There is even a special angle that will cause all reflected light to be polarized.

Most sunglasses today are polarized meaning they only pass light of a particular polarization angle.  Because LED watches only generate polarized light, if you look at an LED watch through polarized sunglasses and then rotate the watch or the glasses, you will see the watch indications disappear as the polarization angle of the lens passes through the zero transmission angle.

A Light-wave Amplification by Stimulated Emission of Radiation (LASER) uses these principles in its creation.  By taking a chamber similar to a fluorescent light pumped full of electrical energy with carefully tuned mirrors spaced in the chamber, a LASER can be created.  If the mirrors are spaced to be an integer number of wavelengths of the natural photons emitted by fluorescence of the gas, polarized light can be reinforced by successive generations of photons created by the gas.

Like any fluorescent light, the gas is energized by passing an alternating electric field across it exciting electrons in the atoms to multiple higher energy levels.  When the electrons relax down to lower energy levels, if a pair of the energy levels has a difference equal to the energy of a visible photon, then a visible photon will be emitted whenever an electron falls down between these steps.  If the mirrors on opposite sides of the chamber are spaced a whole number of wavelengths apart, they can be made to reflect only polarized photons of this wavelength.  It is when these polarized photons interact with an excited atom that they stimulate it to only give off an identical photon, polarized and all.  Basically , the electric field of the incoming polarized photon causes an excited electron to move just as it is moving, kind of like an antennae.  By having the polarized photons bounce back and forth through the gas repetitively, the number of these photons is greatly amplified allowing a coherent beam of the photons to be generated which can then pass through a partial mirror allowing some to exit as the familiar LASER beam. 

The placement of the mirrors requires fairly perfect alignment perpendicular to the beam yet both mirrors must be precisely parallel.  This results in the LASER being created in an extremely straight line making these very useful for industrial applications of projecting linear markers such as for cutting and welding.

When a laser is used for cutting or spot melting, it is through the intense electric field which can be generated by the LASER.  When this interacts with the electrons of a substance which is not transparent, those electrons will be pulled off, then back and forth from the atoms they were previously attached to leaving the atoms without bonding electrons and effectively turning them into a gas.  This only works with high powered LASERS where more energy can be applied to a spot than can be carried away through natural heat dissipation.