This is a great question. Thankfully someone has done the leg work for me and has summarised every single function of the cts: library…
In MarkLogic 6 you can use all XQuery 1.0 and 3.0 predicates and FLWOR constructs. You can also use advanced search functionality, including things like full text search, near searches, custom grammars, and geospatial search. In the below post Evan Lenz talks about all the features available (in 5.0, not 6.0), why you’d use them, and what indexes and DB features you need to enable in MarkLogic:-
http://developer.marklogic.com/blog/grokking-the-cts-api
Don’t forget, there’s also a higher level search: library too that handles grammars and paging for you. Be sure to check that out.
Adam's Deep Technology Blog 