An A-B-C trade just means that website "A" will link to website "B" and website "B" will link to website "C" so that there is no direct reciprocal linking. In this example, you would be the owner of either sites A and C or site B, but not all three, with your trading partner owning the other site or sites.
Some people will do A-B-C-D-E or longer trades, with links going from A to B, B to C, C to D, D to E, etc. Just remember that in this arrangement you need an odd number of sites to come out even.
The idea of "ABC" link trades is a bit of an artifact, sort of like putting your domains on different C-class IP addressess so you can then link them to each other for Search Engine benefits. Once the major search engine(s) had the ability to look up domain registrations, most of the benefit from these kinds of manipulations/techniques began to go away.
More and more, the trend seems to be that if you're not building your links and organizing your sites and trades in ways that are of primary benefit to your surfers, then you can expect most of your efforts to influence SE positions will be in vain.
Or at least that's been my experience.
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