Answer
Metallic emergency blankets work by reflecting a person's body heat back against them. They also work like any other blanket in providing insulation and sheltering from the elements.
Work Step by Step
The shiny blanket has a low value of $\epsilon$, the emissivity.
The person’s body heat is reflected back inward, helping the person stay warmer.
The blanket also reduces convection currents near the person’s skin that would tend to cool the person down, and the blanket also reduces heat loss by conduction.
