Jeton is a French word, and in this context is a numismatic term (numismatics being the study of money and affiliated objects), specifically in the category called exonumia. It is most closely associated in English with the translation "token." We use the term jeton or token to refer to private-issue or unofficial coinage. These are items that typically served a money or money-like purpose, but which were not issued by a government as an official coin of the land. People accepted (or refused) them based on their knowledge of and faith in the issuing person or organization. If a local person down the street made some, perhaps only his friends would accept them, but if a big company issued them, they might find acceptance anywhere people did business with that company. There are two or three major circumstances under which jetons would commonly be created.

1. Lack of sufficient official coinage to meet local needs. In many times and places, particularly on the frontiers of expanding nations/empires, there wasn't a lot of coinage in circulation. Coins are heavy, valuable, and had to be transported across long distances (possibly oceans) in ships to be entered in to distant economies. Rather than being reduced to a strictly barter economy, individuals, businesses, or local governments operating outside the official bounds of their mandate would create their own replacements from whatever metal they could get their hands on - melted down bells, cannons, silverware, etc. The value of coins up until the last century being based on their metal content, these tokens could enter circulation and generally be accepted until (and sometimes after) official coins arrived. They were typically limited only to small denominations, and were used for daily transactions rather than major purchases.

2. To help a business or local economy by keeping money in the area. As mentioned above, people would accept jetons/tokens based on familiarity with and faith in the issuer. If a company issued jetons, and promised to always honor their value, people would continue to spend recirculate those tokens back with the issuing company. If a local government issued them, people would continue to spend them within that local government area. This was especially true if the value honored by the issuer was actually slightly higher than the actual value of the metal. Because a person could get "more for their money" with the issuer than they could if they took it to somebody else who only valued the actual content, they would be encouraged to continue to patronize the business or locality of the issuer. There are some examples from the US during the gold rush of the opposite, where businesses would be set up to issue tokens made of gold (relatively rare, these high-value tokens!) but were found to be putting less than the indicated value in to their product. These issuers swiftly got a bad name and went out of business. The problem of dishonest local issuers is part of the reason a mint now exists in San Francisco.

3. Advertising/propaganda purposes. We've been putting symbols on coins, especially names and faces, for as long as coins have existed. Those symbols serve not only to identify origin and denomination, but to put the message out to the masses about who the local powers are and what they consider important. If you want to reinforce the idea that you are a wealthy, important, contributing citizen, issuing a local token with your likeness and name on it is a great way to remind the populace of your importance. If you are a business in a port city, what better way to make sure visiting sailors and travelers know of and patronize your business than to have tokens in circulation with your name, address, or symbol on them? Money is power, not just in the sense that it can purchase things, but in that the monetary instruments themselves carry symbols and messages to the users.

There are other reasons for the issuance of jetons, and certainly some non-monetary uses like the counting tokens you reference, but for the most part the use of the term jetons refers to unofficial metal "coins" like I describe above. The paper (or occasionally other materials) equivalent would be something like scrip in most cases. It is a fascinating field of study, and there are far more tokens in many places over the years than there are official coin issues, with quantities issued ranging from tens of thousands down to just a handful of any given style, so it's difficult if not impossible to ever know if all the examples from a certain time and place are known. Answering the second part of your question, the reason they are found in a similar manner to coins is that they were used in a similar manner to coins, pretty much everywhere in the world, at some time or another.

Because there are so many examples, from so many places and time periods, I don't know of any books that even attempt to cover them all in a general survey way. There are, however, books focusing on most regions and time periods, and the particular jetons/tokens of those. Amongst the most famous would be the work by James Conder, entitled An arrangement of Provincial Coins, tokens, and medalets issued in Great Britain, Ireland, and the colonies, within the last twenty years, from the farthing to the penny size, which gave rise to the term "Conder Token" to refer to a large grouping of these items (generally 18th century Great Britain and Ireland issues). There are also guides for the American colonies, most European countries, their colonies, and numerous other areas around the world. For general information about the type, most standard numismatic references will have at least a basic outline of what they consider to be a token or jeton.