Scalability can be defined in many ways. However, in general it is the relationship of how an output increases with a change in input. Typically we may think of how throughput changes as we increase the number of CPUs. In a perfect world we would like to have linear scaling. . I came across a good example of non-linear scaling. It is from a presentation presented by Peter Hughes. It is where you are having a dinner party and have 1 meter square tables each table seats 4 people. As it is a dinner party you want to have everybody facing each other as much as possible. So with one table you can sit 4 people.
To increase the number of guests you need 4 tables but you can now only sit 8 people.
To increase the number of guests again you need 9 tables but you can now only sit 12 people.
If you plot the relationship between guests and tables on a graph is looks like the one below.