Chondrites are both the most common and the most important type of meteor to science. Chondrites are nonmetallic stony meteors whose parent bodies never underwent melting or differentiation- essentially, they're largely unchanged in composition and structure from the early days of the solar system. They give us an unrivaled view of the early history of the Sun and the worlds orbiting it.
A thin section view of a barred olivine chondrule from meteorite Begaa NWA 4910 LL3.1 viewed through the cross polar light (xpl) mode of a mineralogical microscope. [Image source]
The study of meteorites is intensely detail oriented- a meteorite researcher (usually a geologist, though there are chemists and physicists who participate as well) will often spend weeks or months poring over a single meteor slice (a thin section) through a geological microscope. They'll record the structures, the minerals, the deformation, and a host of other details about the internal structure of the meteor. (I've done this, it's exhausting and the microscope gives me a headache. I did it on a type of meteor known as ureilite, however, not a chondrite.) They'll then run the sample through various chemical tests.
One of the most interesting results that crop up in chemical analysis of chondritic meteors is their remarkable similarity to the gross elemental makeup and chemical similarity to the sun. It only differs in the lighter elements- notably lithium. This, however, is explained by the fact that lithium isn't generated in the sun- it was only generated shortly after the Big Bang- and the sun tends to destroy it over time. So chondrites have the chemical composition of the sun from long ago. Specifically, from before the sun was born. They're more like the sun than the sun is.
The meteorite Begaa NWA 4910 LL3.1 viewed with the naked eye. [Image source]
This is because chondrites are remnants of the pre-solar dust cloud that the whole solar system formed out of. For a long time the dust cloud just floated in place, since it wasn't dense enough to collapse into a star on its own. Then something changed, and the whole thing began to collapse and coalesce. The leading hypothesis is that the dust cloud was struck by the supernova blast wave of an older star. This hypothesis is backed by chemical analyses- among other proof, chondrites have a large amount of a specific aluminum isotope that is only formed in supernovas. The variations in the composition of the dust cloud would be echoed in the variations in the planets that formed in various regions of the cloud.
Before the planets formed, of course, there was a long period of countless chaotic fragments slamming into one another, melting into a larger body, then being shattered again. The early stages of coalescence, when the Sun was just starting to form, was known as a protoplanetary disc or planetary nebula. Scientists most often refer to them as proplyds.
An artist's impression of a protoplanetary disc. [Image source]
Inside of chondrites are smaller, sand sized or smaller chunks known as chondrules. These rounded grains started off as partially molten droplets in space, and were then accreted into asteroids and other large bodies. The early solar system was filled with a fiery rain of these still molten chondrules. Chondrules are, in a very real sense, the basic building blocks of the solar system. Everything in the solar system is formed from them, but in everything other than chondrites, various chemical, physical, and temperature related processes have altered the chondrules beyond recognition. Like the chondrites to which they belong, chondrules give us an amazing window into the early days of our solar system.
Of course, you can go even farther back in time with materials found in chondrites, to well before the formation of the solar system began. Presolar grains are bits of stardust that got blown into the dust cloud that would become our solar system by the solar winds. They're usually found in the matrix of the chondrites (essentially, the 'cement' between the mineral grains and chondrules), and presolar grains can be differentiated from 'solar' grains by their different isotopic composition. Getting them out, frustratingly, requires the dissolution of the matrix rock via acid or other means.
Protoplanetary discs in the Orion Nebula. We've found more proplyds in the relatively young Orion Nebula than anywhere else. [Image Source]
Comparing the composition of presolar grains and chondrules gives us our absolute best evidence for use in explaining stellar evolution- even over the visual observation of stellar objects our many telescopes do. They're our best teacher about the early solar system. All of us- every planet, every plant, every animal, every rock in the solar system (excepting presolar grains) are from Earth. That fiery rain from the dawn of the solar system gave birth to us all.
Bibliography:
https://en.wikipedia.org/wiki/Presolar_grains#In_meteoritics
https://en.wikipedia.org/wiki/Stellar_evolution
https://en.wikipedia.org/wiki/Cosmic_dust#Stardust
https://en.wikipedia.org/wiki/Formation_and_evolution_of_the_Solar_System#Formation_of_the_planets
https://en.wikipedia.org/wiki/Chondrule#Formation
https://en.wikipedia.org/wiki/Chondrite
https://en.wikipedia.org/wiki/Proplyd
https://en.wikipedia.org/wiki/Protoplanetary_disk
My notes from my Meteorites and Astrogeology classes.
Exploring the Solar System, by Peter Bond.
http://www.skyandtelescope.com/astronomy-news/sun-loses-lithium-with-age/