One of a pair of appendages near the mouth of a chelicerate (spider, horseshoe crab, etc.).
In spiders, they function as extra-sensitive taste and smell receptors. In sexually mature male spiders, they are used to transfer sperm to the female.
Usually used in the plural. I follow an Insect Identification group on Facebook; they seem to post a lot of pics of male spiders with conspicuous pedipalps.
Here is the WIkipedia entry.
And here is a pic of a jumping spider with pedipalps that look like tiny yellow mittens - behind the cut, for anyone bothered by spiders.
Etymology: Latin; peos, foot + palp, touch.