HEMA is short for «Historical European Martial Arts».
There must be about as many definitions for HEMA as there are people doing it (and then some), but very broadly it refers to the study and practice of combat systems of european origin which were codified in period documentation -- in other words: learning how to fight from manuals written by dead masters.
Although some lineages of martial arts commonly accepted as HEMA are still alive and have been transmitted from teachers to students, such as military saber or classical fencing, the overwhelmingly majority of them are not: from the earliest known fightbook --the MS. I.33, or «Walpurgis Fechtbuch» dated in the early XIV - late XIII century onwards-- many books have gathered combat systems whose practice has been lost through the centuries.
The HEMA community is an informal, international aggregation of individuals and grous who work recovering, translating and putting into practice those systems.
You can learn more about HEMA here: