Simple Definition:

Scaling an application simply means making a piece of software capable of handling amounts of data that is more than the software current ability. This is typically done by either redesigning the piece of software or making the hardware it runs on more powerful.

Examples:

A bookstore is using a software program that stores the customer information and the books they purchased. The store is growing in popularity to the point where within one year; the number of customers grew ten times. The software program cannot absorb and store the customer information fast enough due to the growing number of customers. The software engineer will need to “Scale” the bookstore software application to be able to handle the increasing number of customers without delays.