Easton's Bible Dictionary (1897)
The name originally of a narrow strip of territory in Greece, on the north-west of the Peloponnesus. Subsequently it was applied by the Romans to the whole Peloponnesus, now called the Morea, and the south of Greece. It was then one of the two provinces (Macedonia being the other) into which they divided the country when it fell under their dominion. It is in this latter enlarged meaning that the name is always used in the New Testament (Acts 18:12, 27; 19:21; Rom. 15: 26; 16:5, etc.). , proconsul, of Achaia (Acts 18:12).
Smith's Bible Dictionary (1863)
(trouble) signifies in the New Testament a Roman province which included the whole of the Peloponnesus and the greater part of Hellas proper, with the adjacent islands. This province, with that of Macedonia, comprehended the while of Greece; hence Achaia and Macedonia are frequently mentioned together in the New Testament to indicate all Greece. (Acts 18:12; 19:21; Romans 15:26; 16:5; 1 Corinthians 16:15; 2 Corinthians 7:5; 9:2; 11:10; 1 Thessalonians 1:7,8) In the time of the emperor Claudius it was governed by a proconsul, translated in the Authorized Version “deputy,” of Achaia.
Hastings' Dictionary of the Bible (1898) & Schaff's Bible Dictionary
ACHA'IA (trouble), a Roman province in the New Testament times nearly co-extensive with the modern kingdom of Greece. Paul visited the churches in that region. Acts 18:12,Acts 18:27 ;Acts 19:21 ; Rom 15:26 ;Rom 16:5 ; 2 Cor 1:1; 2 Cor 9:2;2 Cor 11:10 ; 1 Thess 1:7,1 Kgs 15:8. For its towns see Corinth, Cenchrea.
Hitchcock's Bible Names (1869)
grief; trouble