Mayor Winston was a city councilman for ten years prior to becoming Mayor and also a borough President for some time. He is a Democrat (this fact is mentioned only in passing, such as brief references to the DNC). He is a liberal and believes strongly in public education.
It is implied, though not stated directly, that Winston ran for mayor at the instruction/coercion of Mike Flaherty, who became his Deputy Mayor for most of his term.
Winston appears to be an intelligent, mature, accountable, understanding, optimistic, righteous, well-mannered, industrious, no-nonsense, sensible, trustworthy, observant, noble, meticulous, assertive, selfless, open-minded, reasonable, warm-hearted, independent, nice, sophisitcated, tidy, outspoken, nurturing and charismatic mayor who has the ability to connect with voters. Much of this is a carefully orchestrated sham by his staff, especially Mike. The Mayor is actually unbalanced in a number of ways. He is childish, vain, outrageously dim and often oblivious to events, such as forgetting he is the mayor. He behaves in very odd ways behind the scenes, and sometimes in front of them. He has little or no self-control, blurts things out (when asked if he would march in the Gay Pride Parade, he replied "What are you? Drunk?") and generally behaves like a child. He is not, however, without a degree of media skill - he is capable of thinking on his feet and 'winging it' at public events when required. The Mayor also suffers from a lack of focus, letting his mind wander from topic to topic almost at random, and often becoming obsessive and carried away with minor, trivial things.
Mayor Winston is totally incapable of functioning without constant help and advice from aides, especially Mike and, later on, Charlie. In some episodes he is shown having difficulty with everyday tasks unless someone helps him.
The Mayor is a big fan of Tom Hanks, as stated in That's Entertainment, when at the Oscar ceremony he votes for Tom Hanks in every category. He is also a huge fan of Charlton Heston, whom he believes he strongly resembles.
The Mayor apparently came to power sometime before the first season. In Season 3 he is re-elected (though this victory is unseen), though his ex-wife Helen campaigned for his opponent. Mike responded by having the special effects people alter the video of the campaign ad so she was hit by a falling piano.
In the show's fourth season, Mayor Winston launched a bid for the United States Senate, running against the unseen Michael Laumann. By the start of Season 5, Winston seems to have abandoned his Senatorial campaign.
In the last season, Mayor Winston is re-elected for a third term. The series ended shortly afterwards.
As with the character of President Bartlet on TV show The West Wing, the mayor was not intended to be a major character but became so popular he was given more screen time.
Because he has such a distant relationship with his daughter (although it should be noted that this is not his fault, as he tried, on numerous occasions, to reach out to her) he seems to respond very well to people viewing him as a father figure. Both of his Deputy Mayors, Mike and Charlie, end up seeing him as a paternal figure in their lives. Although less vocal about it, Charlie seems to respond to him very well as a father figure, in part because his own father (played by Charlie Sheen's real life father Martin Sheen) was never there for him as a child.
Winston is also a Yale University alumnus who majored in Literature as an undergraduate.