Boyd’s Bible Dictionary:
(trouble). Originally a narrow strip of country on north coast of Peloponnesus, but Achaia and Macedonia came to designate all Greece (Acts 18:12,27; 19:21; Rom. 15:26; 2 Cor. 1:1; 9:2; 11:10; 1 Thess. 1:7-8).
Concise Bible Dictionary:
This with Macedonia embraced the whole of Greece in the New Testament; but with the poets Achaia often referred to the whole of Greece. Under the Romans it was divided into two districts, Achaia being a senatorial province. Tiberias united the two districts into an imperial province under procurators; but Claudius again restored it to the senate under a proconsul, so that Luke was correct in calling Gallio a proconsul (ἀνθὐπατος) or deputy (Acts 18:12; 19:21; Rom. 15:26; 1 Cor. 16:15).
Strong’s Dictionary of Greek Words:
Meaning:
of uncertain derivation; Achaia (i.e. Greece), a country of Europe
Potts’ Bible Proper Names:
A brother; grief or trouble:―a country of Europe, Acts 18:12. {Frater}