NWA 2364. Image © T. E. Bunch, 2004
This meteorite is classified as a CV3 - a type of meteorite known as a carbonaceous chondrite (the chondrules are the spherical inclusions dotting the meteorite and are formed from once-molten material). Carbonaceous chondrites are thought to represent the oldest meteorites in the solar system and actually have a chemical composition similar to that found in the photosphere of the sun. CV3 chondrites give us information about the composition and evolution of the early solar system.
CV3 type meteorites also have large calcium-aluminum-rich inclusions (CAIs) typically composed of minerals like anorthite feldspar (CaAl2Si2O8) among others. These types of inclusions can be radioactively dated with uranium-lead (U-Pb) isotopes.
A recent paper in Nature Geoscience presents results indicating that this meteorite is 4,568.2 million years old. That's 4.568 billion years which pushes it back another few hundred thousand years (nothing dramatic, just a refinement of what we already suspected).
So, while I used to tell students the solar system was 4.56 Ga (Ga = giga-annum or billlion or 1,000,000,000 years), now I'll tell them it's likely 4.57 Ga (rounded off).