At the absolutely basic level, solar power is using sunlight to produce energy. The most familiar "generator", for lack of a better term, would be the photovoltaic solar panel. Without delving too far into it, the panel uses the photovoltaic effect to generate power. The panel uses a material, usually silicon, which absorbs sunlight(photons) and converts them into DC(Direct current) electrical power. The power needs to be run through an inverter to be converted into AC(Alternating current) electricity, and it can then be used to power things.
Another approach to solar power is to use the heat generated by sunlight, rather than the sunlight itself. A good example of this is a molten salt power plant. In this case, you get a field of mirrors to all focus light on a tower filled with a molten salt that holds heat very well. This salt can then be used to heat water to steam to power turbines or can be stored away for later, allowing the plant to continue operating when the sun isn't out.
Speaking of operating when the sun isn't out, let's talk about downsides. The most obvious one is that you can't have solar power without the sun. Even the molten salt plants need at least some regular supply of sunlight to work. This means is that solar power is less effective in the wintertime, when the days are shorter, and a poor choice in regions that see frequent storms or ones far to the north or south. Additionally, the initial price of solar panels is high, although it is gradually dropping, and conversion efficiency of sunlight to useable electrical power is fairly low.
Now, then, why is solar such a big deal? First off, it's essentially unlimited energy. The sun isn't going to go away anytime soon. Secondly, and this is the biggest one, the sun provides an absolutely massive amount of energy. The sun is essentially a massive fusion reactor, hundreds of times the size of our planet. To put this in better perspective, think of the power of nuclear fission. Nuclear weapons probably best illustrate the amount of power it has. The most powerful nuclear weapon ever built by human beings, the Tsar bomb, was enough to level a mountain. It had an explosive power of 50 megatons of TNT, 3,300 times more than the bomb used on Hiroshima.
Nuclear fusion, combining two atoms to form a larger one, releases three to four times the energy of nuclear fission. This goes on in the sun, and the end result of the enormous ball of fire at the center of our solar system undergoing fusion at a colossal scale is an output of approximately 90 billion megatons of energy "per second". The amount of power that the Earth requires is about 60,000 megatons per year, so you can see how it makes sense to think that the sun can provide all this power.
Bear in mind that all of this energy given off by the sun does not reach the Earth. The amount that actually strikes the Earth is still enough to give enough power for the entire world for a year. However, consider that a lot of this ground is already inhabited or doesn't make sense to build panels on. There's only so much space on the planet that we can use for solar panels.
This is where a degree of creativity comes in. We have a great deal of open spaces we don't do too much with. Roofs and roads come to mind, why not convert these into solar panels? You might remember earlier how I mentioned an already existing idea to do just that. It's still mostly just an idea, and would require a lot of funding, but who knows? Converting roads into something more useful than just driving surfaces might be what we need.
Sources -
http://solarlove.org/how-solar-cells-work-components-operation-of-solar-cells/
http://cleantechnica.com/2011/09/30/solar-basics-how-do-solar-panels-work/
http://www.solarreserve.com/what-we-do/csp-technology/
http://www.tc.umn.edu/~dama0023/solar.html
http://www.sandia.gov/~jytsao/Solar%20FAQs.pdf
http://www.tsarbomba.org/
https://www.uwgb.edu/dutchs/planets/sun.htm
http://www.txses.org/solar/content/solar-energy-facts-you-should-know
