They used to just be a plural word, referring to a number of people and having the standard reflexive form of themselves – “There were many people in the queue. They were all told to help themselves from the buffet”.
But we are seeing more and more usage of they and them as a singular, to avoid clumsy uses of he/she or him/her followed by himself/herself. Then, by extension from the him – himself or he – himself formation of the reflexive, people are starting to use themself as the reflexive. “If a child is confident, they may be able to help themself to water”.
This does seem to be sensible, and it’s something I think I’ve used myself (there’s another one!) in the past. However: no more! Because, having been asked about this via Twitter, I looked it up and found that actually themself is not regarded as “good English”. And we like good English on this blog, don’t we?
So the reflexive of singular they and them is themselves, and my above example should read: “If a child is confident, they may be able to help themselves to water”.
An easier one, I suppose, in that one is correct and one is incorrect – you don’t have to remember different usages, just not to use themself. Make that we don’t have to remember …