A primary cell is a cell that is designed to be used once and discarded, and not recharged with electricity and reused like a secondary cell. In general, the electrochemical reaction occurring in the cell is not reversible, and so these cells cannot be recharged.
Examples of these Cells are dry Cells, Daniel Cells, etc.

A secondary cell is a cell that is designed to be recharged with electricity and reused many times. In general, the electrochemical reaction occurring in the cell is reversible, and so these cells can be recharged. Secondary cell works Faradays laws of electrolysis.

Both primary and secondary cells are useful for various applications. The primary cell does not reverse the chemical reaction after discharging. Therefore, it can not be reused. On the other hand, the secondary cell reverses the chemical reaction after discharging. Therefore, we can use it over & over again till its useful life exhaust.