International Standard Bible Encyclopedia 
(1) Jason was the host of Paul during his stay in Thessalonica, and, during the uproar organized by the Jews, who were moved to jealousy by the success of Paul and Silas, he and several other "brethren" were severely handled by the mob. When the mob failed to find Paul and Silas, they dragged Jason and "certain brethren" before the politarchs, accusing Jason of treason in receiving into his house those who said "There is another king, one Jesus." The magistrates, being troubled, took security from them, and let them go.
There are various explanations of the purpose of this security. "By this expression it is most probably meant that a sum of money was deposited with the magistrates, and that the Christian community of the place made themselves responsible that no attempt should be made against the supremacy of Rome, and that peace should be maintained in Thessalonica itself" (Conybeare and Howson, St. Paul ). Ramsay ( St. Paul the Traveler ) thinks that the security was given to prevent Paul from returning to Thessalonica and that Paul refers to this in 1 Thessalonians 2:18 .
The immediate departure of Paul and Silas seems to show the security was given that the strangers would leave the city and remain absent ( Acts 17:5-9 ).
(2) Jason is one of the companions of Paul who unite with him in sending greetings to the Roman Christians ( Romans 16:21 ). He is probably the same person as (1). Paul calls him a kinsman, which means a Jew (compare Romans 9:3; Romans 16:11 , Romans 16:21 ).