Production systems are collections of IF-THEN rules. In the simplest case, the rules may be straight S-R rules, mapping directly to some motor action. Usually though, they operate on working memory, adding or deleting clusters of symbols which can then be tested for by other rules. So the rules are usually of the form
IF you have this pattern of symbols in STM THEN add or delete these new symbolsor
IF you have this pattern of symbols in STM THEN carry out this actionEssentially, production systems generalise the notion of stimulus-response system: the response may be not only an action on the outside world, but also a change to mental state.
Technologically, production systems are not very interesting. Most just follow a simple ``forward-chaining'' procedure which enables them to reason forwards from premises to conclusions. Their interest lies in their use as psychological models and once again, Newell has been a major exponent. In moving from GPS to production systems, he has focussed on the issue of control. In computer science, this refers to the way that a program jumps from one statement to another - its ``attention strategy''. Whereas GPS' control strategy was built in to it, the control in a production system is driven much more by the problem and the data we have. So we focus much more than with GPS on the information that's present in memory, and how it guides us in switching from one problem-solving operation to another.
To start, find out how they work. For this, the account on pages 190-199 of volume 1 of [Handbook of AI] is good. They're also described in the final part of [Learning and Problem Solving] and in most AI textbooks.
Now to some cognitive models. Production systems have been used to models childrens' development, and I'll ask you to read on this next. Find a copy of [Computers and Thought 1989]. The start of Chapter 7 places production systems in a psychological context, while pages 226-231 in Chapter 8 describe their use in modelling childrens' subtraction. Follow up with the Young and O'Shea article in Cognitive Science for 1981 that they reference. Note: there is a misprint in the book that sets this article in 1982.
Another view is given in Richard Young's chapter on Production Systems for Modelling Human Cognition in [Expert systems in microelectronic age]. Pay particular attention to the three levels of modelling he distinguishes, on page 43. Young's work on seriation is described at the end of [Learning and Problem Solving]. You should try to hand-simulate at least a few cycles of one of his programs.