PowerPivot is a free extension for Microsoft Excel 2010 and 2013. PowerPivot is a steroid for Excel. It enables Excel to process a massive amount of data.
Excel with PowerPivot enabled can hold millions of rows in a single sheet and that doesn't have a substantial impact on performance. With PowerPivot, Excel becomes a legit Business Intelligence tool.
Power View and PowerPivot are closely intertwined. If you want to create a Power View report in SharePoint, you have to create the model first in Excel. This model is created with PowerPivot.