A Date Picker lets you select a date from a pop-up calendar, and use that date in your spreadsheet.
To format a cell as a date, click on the cell and use Format > Number > Date:
To use date picker in Google spreadsheets, all you have to do is double click a cell that has a date contained in it.
A Date Picker recognizes dates with formats that coincide with the spreadsheet locale. In this case I’ve used the format day/month/year, as used in the UK. If you’d like to use other date formats, set the spreadsheet locale to a different country using File > Spreadsheet settings…