Ghacks takes a look at the purpose of pingsender.exe, a service that's used by Mozilla to collect telemetry data of users of its Firefox browser. Mozilla claims telemetry.exe gets fired up everytime Firefox closes and points out this data is key to identify and fix performance issues that lead to a sub-par browsing experience.
In short: Pingsender is a separate process that Firefox spawns on shut down to send telemetry data to Mozilla.
Firefox users may load about:telemetry in the browser's address bar to check the data that Mozilla is collecting.
Those who don't want to provide Mozilla with data can turn the data off under about: preferences#privacy.
Similar telemetry collection from operating systems like Windows 10 caused a lot of ruckus, so
if you want to disable pingsender.exe for privacy reasons, you can find further instructions over here.