An active worksheet is the worksheet that is currently open. For example, in the picture above, the sheet tabs at the bottom of the window show "Sheet1", "Sheet2", and "Sheet3", with Sheet1 being the active worksheet. The active tab usually has a white background behind the tab name.
While it may be true that some of the things mentioned above could be done in a word processor, spreadsheets have a huge advantage over word processors when it comes to numbers. It would be impossible to calculate multiple numbers in a word processor and have the value of the calculation immediately appear. Spreadsheets are also much more dynamic with the data and can hide, show, and sort information to make processing lots of information easier.