The word 'earpiece' is clearly a joining of the words 'ear' and 'piece', the term was likely initially coined for eyeglasses sooner or later in the 18th century, but in addition, it applies to things like old style phone telephone receivers and doctor's stethoscopes.
The principles of design that was earpiece have existed since that time, so the word 'earpiece' was almost certainly used at that point, although it'd not have denoted the exact same apparatus that we currently think of today. best bluetooth headphones for running of 2016, colloquially referred to as 'earpieces', were first made commercially accessible the early 2000's and since that time, the term has proliferated.
By and large, in the 2010's, the word 'earpiece' tends to send less to headphones and earphones (although it's still technically accurate terminology) and increasingly only denotes Bluetooth headsets. As for the word itself, the word 'ear' is really a derivation of the old English wordare. As the Norse wordeyraand can also be cognate with the German wordohrand the Latinauris it's based on exactly the same root word. The word 'piece' continues to be in use as far back as the 11th Century AD and comes in the Old French wordpece(which is itself of early Gaulish source). It likely also has linguistic ties to the early Welsh wordpeth(meaning 'matter').