An affair is a euphemism for a situation where two people are involved in an illicit sexual, romantic and/or passionate attachment, usually for a limited duration. The term usually implies sexual impropriety, but it is not necessarily the case. (For example, in the classic film An Affair to Remember, the love affair in question is perfectly acceptable from a moral standpoint.)
The euphemism is also applied to marital infidelity where one partner has an outside sexual relationship: a liaison. It is sometimes accompanied by scandal.
Affairs in the political sense typically refer to any kind of involvement in illicit business by any kind by public representatives, such as in the Watergate affair. Like the earlier definition this is not always the case - for example the British Government has a Secretary of State for Foreign and Commonwealth Affairs, which is a perfectly legitimate (and usually honorable) position.
Famous affairs
See also