You can find it in all spreadsheet applications like Microsoft Excel, LibreOffice Calc or Google Docs. In the Help pages of the latter, it is described as:
a small blue box in the lower right corner [of the cell]
Is there any name given to that widget? How do people normally refer to it when talking to other people? For example:
– How do I copy this formula to other cells in the column?
– Just click and drag this [insert name here] downwards.