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The Wikipedia entry Fair exchange has only two lines, and the only paper I can find describing such a protocol is extremely complicated.
Is this a new field in cryptology or can someone give an example of actual use or provide a simple implementation?
Fair exchange protocols aren't new by any means, but there is a lack of layman-friendly material out there, unfortunately. I think the high prevalence of theoretical cryptography in fair exchange protocols may be partially responsible for that.
At any rate, here is the basic idea behind a fair exchange protocol. Suppose you have two parties, Alice and Bob, who wish to trade (cryptographic) "items" somehow. However, you run into a problem: suppose Alice sends her item to Bob, but Bob then refuses to send his item to Alice. In that case, it is not a fair exchange: Bob got Alice's item, but Alice got nothing in return, the poor thing.
Fair exchange protocols seek to ensure that scenario never happens---either they both get each other's "item" or they both get nothing. If the "item" being exchanged fits certain criteria, then fair exchange protocols can be improved upon to have other nice properties, like no longer requiring a trusted third party or being able to detect a dishonest third party.
There are other questions on this site which go into more details about specific fair exchange situations, like
which both link to useful papers. Further, there are some really nice results in the Google results for fair exchange cryptography. Some of them are indeed quite technical in nature, but usually you can read the abstract and maybe the introduction without getting too involved in the mathematical specifics of the protocol in question. One link in particular stands out as being a layman-friendly explanation. The other links should give you some idea of what "items" are traded, often digital signatures. Fair Exchange in E-commerce gives a really nice overview of the field, especially in the first few pages, and also has friendly terminology definitions on page "11" (page 3 of the pdf), defining terms such as "optimistic" fair exchange schemes (which only require a trusted third party to intervene in the event of a cheating player).
