Excel 2013 is a powerful workbook and database application that's included in Office 2013.
Excel has always been an immensely powerful application, if you know how to use it. Microsoft specifically targeted ease of use for Excel 2013. When users input data, Excel 2013 will analyze the type of data it is and will give suggestions about the best way to present the data. If the data is comprehensive enough, it will even analyze it and present an option to make a PivotTable automatically.
There is also a new feature called Flash Fill, which will help put badly formatted data into something comprehensible. Data will be sorted into the appropriate columns for you. This takes so much work out of manually organizing your data that Flash Fill may be the killer feature for those deciding whether to upgrade to Excel 2013.
One big improvement in Excel 2013 is how organic it feels. There are little, quick animations that mimic those found in Windows Phone 8, helping to make the program feel less clinical. The animations aren't distracting and help guide your focus to what Excel is currently doing.
The ribbon interface stays but has been tweaked to be more usable. Icons are different colors and grouped nicely. There is a new option in Excel 2013 to pull in pictures from the web from services that you've linked to your Microsoft account. Setting up Excel 2013 is automatic as it'll pull information from your account.
While Excel 2013 still has an intimidating amount of features, it has become smarter, making it easier to work with data. Microsoft has done an outstanding job with Excel 2013 and anyone who uses Excel on a daily basis should upgrade.