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.
There are lots of spreadsheet packages. What you will want to get depends on what features you need, how much you are willing to spend and what operating system you are using. Google Sheets is free and has most of the basic spreadsheet features, and is accessible online (and you can use your Google Sheets offline too). Microsoft Excel comes as part of the Microsoft Office suite and is one of the most commonly used spreadsheet packages. OpenOffice is free, can run on Linux-based systems, and consumes less memory than Microsoft Office. Lotus 1–2–3 was one of the first and most widely used spreadsheet packages back in the 80’s-90’s but it has been overtaken by Microsoft Excel in terms of popularity.