They were originally meant for accountants to use when working with lots of numbers - they were large sheets of paper with lots of rows and columns. But the usefulness of having formulas do all the adding and multiplying - the tedious part of spreadsheet made VisiCalc, Lotus 1-2-3 and Excel huge hits of the PC.
Nowadays, everyone uses them whenever they want to work with any kind of data. I track my weight and blood pressure in a spreadsheet. A different spreadsheet is used to track my running miles and races, going back 20 years. I track my expense reports, when submitted, when paid - in a spreadsheet. I have another one where I am logging my frequent flyer points. Some people use a spreadsheet, instead of Quicken, to track their personal finances.
Spreadsheets don't have to be used only for numbers. At work, we are gathering requirements from users for a new software project. The requirement is a paragraph in one cell, and then there are dozens of columns next to it with information about that requirement. Can the new tool do it directly or will we need to do some customization. How many manhours to do the customization, person responsible, has the board approved the requirement and the work, date accepted, etc. We now have over 500 requirements (rows), each requirement with dozens of characteristics (columns). (And we will move this whole mess into a Requirements Database soon).
The data in a spreadsheet is often the starting point for other documents. A chart or table from Excel can be embedded into a Word Document or into a PowerPoint presentation - or into an email. While those other tools have simple tables and charts, they don't have the wealth of formulas and formatting options that Excel has.
As an engineer, I now do most calculations, except for highly mathematical ones, in a spreadsheet. Why use a calculator to do arithmetic calculations, when you can punch the numbers into a spreadsheet (same work as punching the numbers into a calculator)? You can more easily double check your work - and if one of the numbers changes, you just update the one number and the spreadsheet does the work of recalulating everything.
A spreadsheet is not always the best way to track data - but it is often where most people start - and when it gets to be too much, they then turn to a database or a specific application. In any Corporation or even small business, there will be important data in dozens or hundreds (or thousands) of spreadsheets, on server shares and on peoples PCs spread who knows where all over.
A person who takes the time to learn how do use the capability of Excel is a valuable asset, in a company - and is well respected by their colleagues. Every four or five years, usually when a new version of Office comes out, I take a couple weekends to read a book on the new version - and always learn more - usually about a capability that has been there, but I had forgotten or did not realize the significance.