This display illustrates the idea of herd immunity, with a simple model where each person is connected to four others, above, below, left, right. Yellow means the person is susceptible (has not had the disease), and blue means the person is immune and cannot have it again. Click in the grey bar to change the proportion of people that are immune. At first everything is static: there is no infection because there are no infected people.
Now click on the grid, introducing a single infected person, and watch it spread. Notice that when the immune percentage is low, the infection spreads rapidly, but if the percentage is above 60 or so, the infection does not spread widely. This is herd immunity.
For more information, see the Wikipedia entry on Percolation Theory