To simper means to smile in an artificial, coy or self-conscious way. If you hope to please someone by simpering, you may wind up annoying him or her.
The origin of the word simper is not clear, but it is probably Germanic as there are similar words in Danish as well as Middle Dutch. What is clear is that a simper is not attractive to those observing it. Watching your colleague simper and giggle as the boss tells a not-very-funny joke, you can be sure that she is angling for that promotion.