There's no such thing as a true "simple" explanation. In some ways, these are some of the most complicated electronic devices around. (in some ways though, they're actually some of the simplest). When I have some time later this week, I'll write some stuff up.
bobhaha hit some of the high points, but as they say, the devil is in the details.
Lasers are MUCH more complicated than regular p-n diodes: in structure, in the materials they're made of, and in the physics.
In materials: Laser diodes aren't ever made of silicon (although bobhaha did correctly point out the doping materials used in silicon, giving you an idea of how doping works, with P or B sitting on Si sites and contributing holes or electrons). Laser diodes use III-V semiconductors. Si is a group IV semiconductor (look at your periodic table), you can see it's neutral and highly covalent in nature, with each Si sharing its 4 electrons with its 4 nearest neighbors, giving full valence of 8 electrons per atom. By combining a group III element (like gallium) with a group V element (like nitrogen), you see how you get the same thing, with full valence for each atom and highly covalent bonding. But with a III-V semiconductor, you can see how doping gets more complicated. The material is even more complicated because it's rarely ever just 2 elements, it's often alloys like InGaN, InGaAsP, etc. Still charge-neutral III-V highly-covalent solids, and then doped to p- or n-type, but much more complicated.
In structure: Laser diodes aren't simple p-n diode. They're typically p-i-n diodes (i meaning intrinsic, or not doped), and typcially quantem wells at that. Additionally, they're heterostructures, meaning the p-type region is a completely different material from the i-type region, which is a completely different material from the n-type region. For example, an InGaN "intrinsic" (actually unintentionally doped, but beyond the scope of this discussion) region sandwiched between p-type and n-type GaN layers. It's a quantum well because the InGaN layer will only be single-digit nanometers thick.
In the physics: Well, you get the idea.
So yeah, maybe later I'll type up a full, real response on how electrons and holes combine to make coherent light, when I have some more time. At least you have some more topics to start with now, in the mean time.
