yum makes me hungry for a mesh of bacon
 

Don't laugh at me, but what IS this mesh stuff and how do I start to learn it?
 

With prims you make simple shapes into complex linksets; with sculpties you can *sort of* and in a frustrating way in many cases make one object that has a more organic shape. Sculpties are like a kind of trick to make the viewer see 3d model data.
Mesh is what our world is made of: the ground, avatars, slider skirts and hair - they are mesh (I'm leaving prims and sculpties out to avoid being confusing). Up until now we haven't been able to directly import mesh models, but now it's on its way. You can model anything including an avatar (avatars need to be rigged to replace our avatars). Models have a cost and equal whatever number of prims LL thinks is fair for the streaming cost (which is good).
If you, say, make a meerkay model and rig it for avatar use, and you sell it, that avatar is less configurable than, say, a mod avatar made of prims.
Models can have up to 8 textures, I believe.
Some free 3d programs are SketchUp, MeshLab, Wings3D, Blender, and Sculptris. Blender is notoriously brain-exploding. I've used Wings3D a ton for making sculpties, and it's good - if I used it more often I'd be further along. SketchUp is pretty awesome, and I think you'd find it fun. Sculptris is more than fab. Since Pixologic recently hired its creator and folded it into its product I suspect that bodes ill for Sculptris. But it's still available.
 

Judge Dredd!