Meyer lemons are a bay area staple; all over recipes in cook books from Chez Panisse and the restuarants of Chez Panisse alums. It is easiest to describe the flavor of these lemons in relation to more familiar varieties. They are less tart, less brightly acidic, have a thinner skin, and are more sweet.
According to the Splendid Table, the lemon variety was introduced to California in 1908 by Frank Meyer, a "plant explorer" for the U.S. Department of Agriculture. Peak season in most areas is November, December, and January, but can extend to April.
As they ripen, the yellow skin of Meyer lemons becomes more golden, even slightly orange. Scientists speculate that the lemon is actually a hybrid of lemon and oranges, possibly mandarins. The Splendid Table maintains they were found growing near Peking. Four Winds suggests that the species was used decoratively in door ways - of course they also describe the flavor as mystical.
Similar to my sense of Fuji apples, I maintain that experience of eating a Meyer lemon has less to do with it being exceptionally sweet than it does a depth of taste and flavor that borders on savory.
A woman I work with brought these lemons into the office. At the time they were bright yellow, and the skin felt thicker than I was accustomed to. I speculated that they might be Lisbon lemons, and over the course of a day squirreled away six of them.