So what is a ductile material and what is a brittle material? Simply a ductile material is a material that will typically deform when a large amount of energy is absorbed into the material during short period of time, while a brittle material will instead shatter when a large amount of energy is absorbed into the material in a short amount of time.
So what makes a material ductile? A material that is ductile has the ability to deform and essentially absorb quite a bit of energy before it will break. If you were to look at the stress strain plot of a ductile material it would have a very large plastic area that allows quite a bit of strain before the material reaches its fracture stress . There will also be large amount of necking before the material fails.
Unlike ductile material, a brittle material will have a very small plastic region in comparison. Due to this fact once a brittle material leaves the elastic region it will fail a lot quicker. The break will also be a lot cleaner since there will be less necking.
The images below show what a ductile material break would be in comparison to a brittle material. They also show what the stress strain curves would look like.