I don't like it; it's not to my taste. Can be used in a variety of ways, such as in reference to activities (skiing isn't my cup of tea) or people (he's not my cup of tea).
Unsurprisingly, this expression originates in Britain in the first half of the 20th century. But long before that, at least as far back as the mid 18th century, the affirmative version was in use. In fact, according to phrases.org.uk, "cup of tea" was such a synonym for acceptability that it became the name given to a favored friend, especially one of ebuliant nature. From the use of it in William de Morgan's 1908 novel Somehow Good, it can be assumed that the expression started as one used by the working class:
"He may be a bit hot-tempered and impulsive... otherwise, it's simply impossible to help liking him." To which Sally replied, borrowing an expression from Ann the housemaid, that Fenwick was a cup of tea. It was metaphorical and descriptive of invigoration.
By 1932, Nancy Mitford clearly felt able to use the expression in her comic novel Christmas Pudding, without need of explanation:
I'm not at all sure I wouldn't rather marry Aunt Loudie. She's even more my cup of tea in many ways.
According to Gregory Titelman's America's Popular Proverbs and Sayings, the negative form has been in use since about the 1920s, but it appears to have caught on during the 1940s during World War II. One can't help wondering if this was due to the many Americans in Britain who likely found the nation's favorite beverage not to their taste!
In 1944, Hal Boyle wrote in his syndicated column, Leaves From a War Correspondent's Notebook that in England, "You don't say someone gives you a pain in the neck. You just remark 'He's not my cup of tea.'"