Agate is quartz that grew as microscopic fibres rather than visible crystals, deposited in bands inside a cavity. The banding is a growth record, laid down layer by layer as silica-rich water passed through, which is why the bands are concentric and follow the shape of the void they filled.
It behaves like quartz because it is quartz: hardness 7, no cleavage, conchoidal fracture, inert to acid. What differs is the lustre, which is waxy or resinous rather than glassy, because the surface is a mat of fibre ends rather than a single crystal face.
The thing to know before buying is that agate is dyed on an industrial scale, and has been since the nineteenth century when the trade at Idar-Oberstein in Germany perfected the process. Bright blue, purple, green, magenta and neon-pink agate slices do not occur naturally. They are dyed, and the trade has been open about it for two hundred years — which does not stop them being sold as natural.