Spreadsheets are, in many ways, the application that launched the personal computer into the business world. The very first spreadsheet, VisiCalc, was created for the Apple II line of computers and was an immediate success. Lotus was the first company to bring the spreadsheet to the IBM PC compatible with Lotus 1-2-3, and other vendors quickly followed with their own versions of the application.
Spreadsheets are more popular than ever today, often being found as the cornerstone of what People Who Like Big Words call "Administrative Support Systems". Even a simple spreadsheets give a person enormous power to keep track of how money and information flows through a company, or to rapidly try out several values (for a product price or a test curve, for example) and see the ramifications of each one.
Spreadsheets, more than anything else, were at the heart of the first "look and feel" lawsuits. As more companies made spreadsheets, the question came before the courts: Can you copyright or patent the 'look and feel' of a program -- the way it appears to the user and the keys you need to press -- even though other people are writing their own programs from scratch? The answers have been ambiguous and mixed over the years, but the general idea currently is that you can copy another program's "look and feel" (within reason) without getting sued.
A spreadsheet is a way to set up relationships between numbers.
Sure, a spreadsheet will make graphs and do arithmetic and create really good-looking tables, but most of that is just snazzy extras. The heart and soul of a spreadsheet is its ability to let you set up relationships between sets of numbers, and then play with the numbers to see what happens.
By setting up correct relationships between the different values, we give ourselves the ability to "play" with the actual numbers to see what happens.
Spreadsheets are most powerful when we're using them to answer "what if" questions. Since we're setting up relationships between numbers, we can change a single number and see what it does to all the other numbers.
Before spreadsheets, when all this sort of information was kept on paper, you couldn't change things around or answer questions without an enormous amount of work. Now, a couple keystrokes can give you an answer in less than a second.