What is this white fitting inline with my showerhead?
Probably a charcoal filter. Probably disgusting (people put them in, change the filter a few times, and then get bored of buying the filters, which turn into a gross mess as often as not.) Or the filters become unavailable since these are not exactly a standard item.

I'd strongly suggest removing it; if you want to keep it and can find filters for it, at least take it off and clean it throughly and replace the filter.

Looks like perhaps this one: