I first came across this term in §39 of Wittgenstein's Philosophical Investigations, wherein he writes
[O]ne is tempted to make an objection against what is ordinarily called a name. It can be put like this: a name ought really to signify a simple.
He then provides the example of the word Excalibur, which is a proper name of the sword Excalibur. The sword, being a particular combination of parts, ceases to exist if said parts are combined differently. If such a rearrangement were to take place, Excalibur would no longer exist. But if Excalibur is broken up, the proper name Excalibur no longer refers to anything. A sentence like "Excalibur has a sharp blade" therefore contains a word without meaning; it shouldn't make sense, yet it does.
Wittgenstein follows this by saying
there must always be something corresponding to the words of which it consists. So the word "Excalibur" must disappear when the sense is analysed and its place taken by words which name simples. [emphasis added]
The argument he is making for the most part makes sense to me, but I do not know what simples are. Some cursory Googling led me to articles about logical atomism and concepts such as "atomic facts," which apparently consist of one or more "simple particulars." I also found mention of "designated simples," which are components of an ideal language promoted by logical positivists.
I have no idea whether these concepts are related to the simples Wittgenstein is discussing or even to each other. Any clarification would be appreciated.