Jess,
First off welcome to the forum...Lots of great info here and most are more than willing to help someone out.
On the main Hearth.com home page is the Main Articles link. About middle of right side of page.
Hit that and then scan down to
Pellet/Corn/Biomass Appliances.
There you will find a bunch of basic info articles that might help you out
Here is a quick picture labeling the various Pellet stove parts.
View is from front of stove.
Basically there are two air movement systems in the stove.
Combustion (the Fuel and fire side) and Convection (The turn the cold air into warm air)
Basically fuel (Wood Pellets) are stored in the hopper. At the bottom of the hopper is a screw auger that "lifts" the fuel up so that it can fall into the fire box where it feeds a burning fire. Exhaust gasses are circulated past some heat exchanger tubes and are sucked out to the "Venting" pipe to outside via an exhaust blower. There are some electronic controls to keep all of this continuing safely and efficiently.
The Convection Blower takes "Colder" room air and pumps it thru the inside of the heat exchanger tubes and makes it hot(er). Dispersing it into your living space.
Most modern stoves use an electric igniter to start the initial fire but they can also be started manually using starting gel or a propane torch.
Newer stoves control almost all aspects of the burn cycle regulating blower speeds, fuel feed rates, and even are run on thermostats. Older stoves rely on temperature snap disks and manual controls. Nothing wrong with either its just a matter of convenience. More "bells and whistles"
Hope that gets you started.
Good Luck,
---Nailer---