The word “Harwicensis” is simply Latin for “[of] Harwich”. The word would occassionally be used as, back in the day, Latin was still a common language, and would regularly be used instead of – and alongside – English.
Many early parish registers used both Latin and English, where there would be a period of one followed by a period of the other. Sometimes it would be because a different clerk took over record-keeping duties, other times the same clerk would switch between the two, perhaps depending on outside factors of the time.
Harwich was no different. In 1608, John Cutting, the first appointed Steward of the Borough of Harwich (as chosen in the Royal Charter of King James I in 1604) died, and his burial record describes him as “Burgi Harwicensis Senescallus”, which translates to “Steward of the Borough of Harwich”.
Another common variant of the time was “Herewici”, as was written in the aforesaid Charter. This was back before standardised spellings, so it was the Latinised version of “Herewich”, as Harwich was commonly spelt in Medieval times.