From BiblePortal Wikipedia

Morrish Bible Dictionary [1]

The persons who farmed the taxes levied by the Romans, a certain sum being payable for each district. These then farmed out smaller portions to others, or engaged them to collect the money. The whole system was bad, and was capable of abuse by the collectors demanding more than they should. The counsel given by John the Baptist to the Publicans was: "Exact no more than that which is appointed you."  Luke 3:12,13 . Zacchaeus would appear to have been a just and liberal man; he speaks of restoring money taken 'by false accusation': being 'the chief among the publicans,' he remedied such things as were under his control.

The obligation to pay taxes to the Romans was very galling to the Jews, and those engaged in collecting them were accounted unworthy of any respect, hence 'publicans and sinners' are often classed together; the Lord was derided by the religious people for entering their houses: they mockingly called Him "a friend of publicans and sinners." But God's grace was for all, and Matthew was called from his office of publican to be one of the apostles.  Matthew 5:46,47;  Matthew 10:3;  Mark 2:15,16;  Luke 5:27-30;  Luke 18:10-13 .

The Nuttall Encyclopedia [2]

name given by the Romans to persons who farmed the public revenues; specially a class of the Jewish people, often mentioned in the New Testament, and specially odious to the rest of the community as the farmers of the taxes imposed upon them, mostly at the instance of their foreign oppressors the Romans, and in the collection of which they had recourse to the most unjust exactions. They were in their regard not merely the tools of a foreign oppression, but traitors to their country and apostates from the faith of their fathers, and were to be classed, as they were, with heathens, sinners, and harlots.