Kitto's Popular Cyclopedia of Biblial Literature
Acha´ia, a region of Greece, which in the restricted sense occupied the north-western portion of the Peloponnesus, including Corinth and its isthmus. By the poets it was often put for the whole of Greece, whence Achaioi, the Greeks. Under the Romans, Greece was divided into two provinces, Macedonia and Achaia, the former of which included Macedonia proper, with Illyricum, Epirus, and Thessaly; and the latter, all that lay southward of the former. It is in this latter acceptation that the name of Achaia is always employed in the New Testament (Acts 18:12; Acts 18:27; Acts 19:21; Romans 15:26; Romans 16:5; 1 Corinthians 16:15; 2 Corinthians 1:1; 2 Corinthians 9:2; 2 Corinthians 11:10; 1 Thessalonians 1:7-8). Achaia was at first a senatorial province, and, as such, was governed by proconsuls. Tiberius changed the two into one imperial province under procurators; but Claudius restored them to the senate and to the proconsular form of government. Hence the exact and minute propriety with which St. Luke expresses himself in giving the title of proconsul to Gallio, who was appointed to the province in the time of Claudius (Acts 18:12).
Kitto, John, ed. Entry for 'Achaia'. "Kitto's Popular Cyclopedia of Biblial Literature". https://www.studylight.org/encyclopedias/eng/kbe/a/achaia.html.