When a person is resilient, we mean that they bounce back from change to their original personality. Resiliency in the material sense is similar. We can define resilience of the material to be the amount of energy the material can absorb and still return to its original state. If we are talking about stressing the material and having it return to its original state, we are talking about the material remaining in the elastic region of the stress-strain curve. It turns out that we can get the energy of elasticity by taking the area under the curve of the stress-strain curve. That area has been highlighted in the figure below, which is the area under the curve from the origin to the yield strength.
Toughness, in contrast to resilience, is how much energy can be absorbed and still keep going. One analogy that can be used when describing toughness is that of a car in a demolition derby. The car is allowed to continue the competition as long as it is capable of moving. It does not matter how many hits and how much destruction has been done to the car, but rather as long as the car can move it can stay in the competition. The toughness of the car is based on how many hits and how much damage the car can sustain and continue in the competition. In the case of materials, the amount of energy that the material can absorb plastically before fracturing is the toughness.
In the figure below, we can see that a material can have a high tensile strength (ceramics) and yet have a small toughness. In addition, materials can be extremely ductile (unreinforced polymers) and also have a small toughness. So, a large toughness (metals) is obtained by having a high tensile strength and a high ductility.