Can you explain how vaccination could eradicate a disease such as smallpox?

Herd immunity

Explanation:

It is important for people (especially children) to be vaccinated when recommended by doctors and nurses. Smallpox is a disease that causes extreme swelling in its victims. This disease can only be transmitted from person-to-person through direct contact, and using this knowledge and vaccines, it was relatively easy to eradicate.

Building up immunity in a population is known as herd immunity and stops the spread of deadly diseases by reducing the chance that a non-vaccinated person is in contact with a sick person (or another non-vaccinated person).