Well I don't know how much physics you know so I'll try and keep it fairly basic. Laser is an acronym for Light Amplification by Stimulated Emission of Radiation. What does this mean? Well the most important part to understand is the concept of stimulated emission and how it produces coherent light. When I'm talking about coherent light I'm referring to light which is in quite well in phase (where the wavelengths line up) and travelling in the same direction. These two properties give laser light their extraordinary characteristics.
Back to stimulated emission though, say we had a material which you could excite with some kind of energy (let's say its a crystal) which would release a bit of heat then stay mostly excited. Now eventually the atoms in the crystal randomly emit light and this makes them unexcited again but we choose a material where this process tends to happen slowly. The crystal we have chosen exhibits the property of being suitable for stimulated emission which means that when a photon (the smallest bit of light you can have) passes through the crystal it will soon encounter one of the atoms you have excited and when it does it makes the atom emit a bit of light and become unexcited as above. The cool thing is that now you have two photons of light travelling in the same direction with the same wavelength (which is colour). So now we have a way of making pulses of coherent light. We excite a crystal, when one of the atoms randomly emits light it travels through the crystal gathering more photons and making a bit of a laser. Cool.
Unfortunately this way will only give you really small and weak pulses. You improve this by putting the material in a tube with both ends as mirrors, the trick being that one of the mirrors is semi reflective. Now when your pulse of light exits the crystal it will be reflected back through the crystal and soon we'll have a continuous stream of coherent light bouncing between the two mirrors with a proportion going through the semi reflective one and outside into the real world as your laser!
For a visual example see this small java thing.
Depending on your level of physics knowledge ignore the graphs on the right and just look at how the stimulated emission builds up a resonant stream of light.
Hope that helps.